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Boston Public Library
PURCHASED FROM THE
James Lyman Whitney
MEMORIAL FUND ESTABLISHED BY
James Lyman Whitney
BIBLIOGRAPHER
AND SOMETIME LIBRARIAN
LETTERS
OF
EULER
ON DIFFERENT SUBJECTS
IN
PHYSICS AND PHILOSOPHY.
ADDRESSED TO
A GERMAN PRINCESS.
TRANSLATED FROM THE TRENCH BY
HENRY HUNTER, D.D.
WITH
ORIGINAL NOTES,
And a Glojfary of Foreign and Scientific Terms:
4beconD €irition.
IN TWO VOLUMES.
VOL. II.
EonDon :
PRINTED FOR MURRAY AND HIGHLEY ; J. CUTHELL ; VERNOR
AND HOOD; LONGMAN AND REES ; WYNN AND SCHOLEY ;
G. CAWTHORNJ J. HARDING; AND J. MAWMAN,
1802.
..y- x
Salisburj'-S'jiiwe.
CONTENTS
OF THE
SECOND VOLUME.
Letter Page
I. • /CONTINUATION of the Subjea, and of
V.^ Miftakes in the Knowledge of Truth I
II. Firfr Clafs of known Truths. Conviction that
Things exift externally correfponding to the
Ideas reprefented by the Senfes. Objection of
the Pyrrhonifts. Reply.' - 5
III. Another Objection of the Fyrrhonifts againft the
Certainty of Truths perceived by the Senfes.
Reply ; and Precautions for attaining Affur-
ance of fenfible Truths 8
IV. Of demonstrative, phyfical, and particularly of
/ moral Certainty - - 12
V. Remarks that the Senfes contribute to the Increafe
of Knowledge ; and Precautions for acquiring
the Certainty of Hiftorical Truths - 16
VI. Whether the Effence of Bodies be known by us 20
VII. The true Notion of Extenfion - 24
VIII. Divisibility of Extenfion in infinitum - 27
IX. Whether this Divisibility in infinitum takes Place
in exifting Bodies r - - 31
X. Of Monads - - 35
XI. Reflections on Divisibility in infinitum, and on
Monads • - "39
Vol, II. A XII. Reply
v. CONTENTS.
Letter , j
XII. Reply to the Objections of the Monadifls to
Divifibility in infinitum <-
XIII. Principle of xhzfatisfyingReafon, the ftrongeft
Support of the Monadifts
XIV. Another Argument of the Monadifts, derived
from the Principle of the fufficient Reafon.
Absurdities refulting from it
XV. Reflections on the Syftem of Monads
XVT. Continuation
XVII. Conclufion of Reflections on this Syftem
XVIII. Elucidation refpecYing the Nature of Colours
XIX. Reflections on the Analogy between Colours
and Sounds
XX. Continuation
XXI. How opaque Bodies are rendered vifible
XXII. The Wonders of the Human Voice
XXIII. A Summary of the principal Phenomena of
Electricity
XXIV. The true Principle of Nature, on which are
founded all the Phenomena of Electricity
XXV. Continuation. Different Nature of Bodies
relatively to Electricity
XXVI. On the fame Subject
XXVII. Of pofijive and negative Electricity. Expla-
nation of the Phenomenon of Attraction
XXVIII. On the fame Subjeft
XXIX. On the electric Atmofphere
XXX. Communication of Electricity to a Bar of
Iron, by Means of a Globe of Glafs
XXXL Ele&rifation of Men and Animals
XXXII. Diftin&ive Character of the two Species of
Electricity - . -
XXXIII. How the fame Globe of Glafs may furnifh,
at once, the two Species of Electricity
XXXIV. The
'age
43
46
5°
53
57
61
65
69
73
76
79
83
87
91
95
99
103
106
in
"5
119
122
CONTENTS. Vii
Letter Page
XXX IV. The Leyden Experiment - 125
XXXV. Reflections on the Caufe and Nature of
Eledtricity, and on other Means proper to
produce it - - - 129
XXXVI. Nature of Thunder : Explanations of the
ancient Philofophers, and of D ef cartes :
Refemblance of the Phenomena of Thun-
der, and thofe of Electricity - 133
XXXVII. Explanation of the Phenomena of Lightning
and Thunder - - 136
XXXVIII. Continuation - - 140
XXXIX. The Poffi'uility of preventing, and of avert-
ing the Effects of Thunder - 143
XL. On the celebrated Problem of the Longi-
tude : General Defcription of the Earth,
of it's Axis, it's two Poles, and the Equa-
tor 150
XLI. Of the Magnitude of the Earth; of Men-?
dians, and the fhorteft Road from Place
to Place - - 154
XLII. Of Latitude, and it's Influence on the Sea-
fons, and the Length of the Day 159
XLIII. . Of Parallels, of the Firft Meridian, and of
Longitude - - 163
XLIV. Choice of the Firft Meridian - 167
XLV. Method of determining the Latitude, or the
Elevation of the Pole - 171
XLVI. Knowledge of the Longitude, from a Calcu-
lation of the Direction, and of the Space
pafled through ■ •■■«. - 176
XLVII. Continuation. Defects of this Method 180
XLVIII. Second Method of determining the Longi-
tude, by means of an exacl: Time-Piece 184
XLIX. Continuation, and farther Elucidations 188
K% L. Eclipfes
V1U
Letter
L.
LI.
LTI.
LIII.
LIV.
LV.
LVI,
LVII.
LVIIL
CONTENTS.
Page
lix?
LX.
Lxi.
LXII.
LXIII.
LXIV.
J.XV.
Eclipfes of the Moon, a third Method of find..
ing the Longitude
Obfervation of the Eclipfes of the Satellites of
Jupiter, a fourth Method of finding the
Longitude - -
The Motion of the Moon, a fifth Method
Advantages of this laft Method ; it's Degree
of Precifion - r
On the Mariner's Compafs, and the Proper-
ties of the Magnetic Needle -
Declination of the Compafs, and Manner of
obferving it -
Difference in the Declination of the Com-
pafs at the fame Place
Chart of Declinations ; Method of employ-
ing it for the Difcovery of the Longitude
Why does the Magnetic Needle affect, in
every Place of the Earth, a certain Direct
tion, differing in different Places ; and for
what Reafon does it change, with Time,
at the fame Place ?
Elucidations refpedYing the Caufe and Varia-
tion of the Declination, of Magnetic Nee-
dles -
Inclination of Magnetic Needles
True Magnetic Direction ; fubtile Matter
which produces the Magnetic Power
Nature of the Magnetic Matter, and of it's
rapid Current. Magnetic Canals
Magnetic Vortex. Adtion of Magnets upon
each other .«
Nature of Iron and Steel. Manner of com-
municating ro them the Magnetic Force
Action of Lqadftpnes on Iron. Phenomenon
pbfervable
"93
197
201
205
209.
214
217
222
226
230
234
239
243
247
25*
CONTENTS.
Letter
LXVI.
Lxvir.
LXVIII.
Page
255
260
264.
268
LXIX.
LXX,
LXXL
JLXXII,
iXXIII.
LXXIV.
LXXV.
LXXVI.
LXXVII.
LXXVIII
LXXIX.
LXXX.
LXXXI.
obfervable on placing pieces of Iron near a
Loadftone
Arming of Loadftones
Action and Force of armed Loadffones
The Manner of communicating to Steel
the Magnetic Force, and of magnetizing
Needles for the Compafs: the Simple
Touch, it's Defeats ; means of remedying
thefe -
On the Double Touch. Means of preferving
the Magnetic Matter in magnetized Bars 273
The Method of communicating to Bars of
Steel a very great Magnetic Force, by
means of other Bars which have it in a
very inferior degree
ConftrucYion of artificial Magnets in form
of a Horfe-fhoe •»
On Dioptricks ; Inftruments which that
Science fupplies : ofTelefcopes and Mi-
crofcopes. , Different Figures given to
Glaffes or Lenfes
Difference of Lenfes with refpecr. to the
curve of their furfaces. Distribution of
Lenfes into three claffes ■*• 290
Effe6l of Convex Lenfes - 204
The fame Subject : Difiance of the Focus
of Convex Lenfes
Difiance of the Image of Objects
Magnitude of Images
, Burning Glaffes
The Camera Obfcura'
Reflections on the Reprefentation in the
27S
2S2
286
298
302
306
310
3l3
Camera Obfcura
;iS
Of the Magic Lantern, and Solar Microfcope 322
6 LXXXII. Ufe
Letter
LXXXII.
lxxxiii.
LXXXIV.
LXXXV.
LXXXVI.
LXXXVII.
LXXXVIII
LXXXIX.
XC.
XCI,
XCII.
XCIII.
XCIV.
xcv.
342
345
350
353
XCVI.
XCVII.
XCVIII.
CONTENTS.
• Page
Ufe and Effect; of a fimple Convex Lens 326
Ufe and/Effect of a Concave Lens 330
Of apparent Magnitude, of the Vifual
Angle, and of Microfcopes in general 334
Eflimation of the Magnitude of Objects
viewed through the Microfcope 338
Fundamental Proportion for the conftruc-
tion of fimple Microfcopes. Plan of
fome fimple Microfcopes
Bounds and Defects of the fimple Micro
fcope
On Telefcopes and their Effect:
Of Pocket-Glaffes
On the magnifying power of Pocket Glaffes 357
Defects of Pocket- Glaffes. Of the appa-
rent Field - - 362
Determination of the apparent Field for
Pocket-Glaffes •» 367
Aftronomical Telefcopes, and their magni-
fying Powers - " - 371
Of the apparent Field, and the Place of
the Eye - - 37.4
Determination of the magnifying Power of
Aftronomical Telefcopes, and the con-
ftruction of, a Telefcope which fhall
magnify Objects a given Number of
Times - - 379
Degree of Clearnefs - 383
Aperture of Objective Lenfes 387
On Diftinctnefs in the Expreffion : On
the Space of Diffufion occafioned by the
Aperture of Objective Lenfes, and con-.
Jidered as the fir ft Source of want of Dif-
tinctnefs in the Reprefentation
XCJX. Dimi
39?
CONTENTS. xi
Letter Pag<
XCIX. Diminution of the Aperture of Lenfes, and
other Means of leffening the Space of Diffu-
fion, till it is reduced to nothing 396
C. Of Compound Objective Lenfes • 401
CI. Formation of Simple Objective Lenfes 405
CII. Second Source of Defect, as to Diftinctnefs of
Reprefentation by the Telefcope. Different
Refrangibility of Rays - 410
CIII. Means of remedying this Defect by compound
Objectives - - 414
CIV. Other Means more practicable - 418
CV. Recapitulation of the Qualities of a good Tele-
fcope - . - - 422
CVI. Terreftrial Telefcopes with four Lenfes 426
CVII. Arrangement of Lenfes in Terreftrial Telefcopes 430
CVIII. Precautions to be obferved in the conftruction
of Telefcopes. Neceffity of blackening the
infide of Tubes. Diaphragms - 433
CIX. In what maimer Telefcopes reprefent the Moon,
the Planets, the Sun, and the fixed , Stars.
Why thefe la ft appear (mailer through the
Telefcope than to the naked Eye. Calcula-
tion of the Diftance of the fixed Stars, from a
Comparifon of their apparent Magnitude with
that of the Sun - - 437
CX. Why do the Moon and the Sun appear greater
at rifing and fetting, than at a certain eleva-
tion? Difficulties attending the Solution of
this Phenomenon - - 441
CXI. Reflections on the Queftion reflecting the
Moon's apparent Magnitude: Progrefs to-
ward a Solution of the Difficulty. Abfurd
Explanations - - aa±
CXII. An Attempt toward the true Explanation of the
Pheno-
XII
Letter
CXIII.
CXIV.
cxv.
CXVI.
CXVII.
CXVIII
CXIX.
CONTENTS;
Page
Phenomenon : the Moon appears more dis-
tant when in the Horizon, than when at a
great Elevation - - 448
The Heavens appear under the Form of an
Arch flattened toward the Zenith 452
Reafon affigned for the Faintnefs of the Light
of Heavenly Bodies in the Horizon 456
Illufion refpefting the Diftance of Objects, and
the Diminution of Luftre - 463
On the Azure Colour of the Heavens 463
What the Appearance would be, were the Air
perfectly tranfparen-t - - 467
Refra£bon of Rays of Light in the Atmofphere,
aod it's Effects. Of the Twilight. Of the
apparent riling and fetting of the Heavenly
Bodies - - - ■ - 471
The Stars appear at a greater Elevation than
they are. Table of Refraction -. 475
LETTERS
letters
ON
DIFFERENT SUBJECTS
IN
PHYSICS AND PHILOSOPHY.
LETTER I;
Continuation of the Subjecl, and of Mi/lakes in the
Knowledge of Truth.
Madam,
THE three claffes of truths which I have how un-
folded, are the only fources of all our know-
ledge ; all being derived from our own experiences
from reafoning, or from the report of others.
It is not eafy to determine which of thefe three
fources contributes moil to the increafe of know-
ledge. Adam and Eve mull have derived theirs
chiefly from the two firft j God, however, revealed
many things to them, the knowledge of which is to
be referred to the third fource, as neither their own
experience, nor their powers of reafoning, could have
conducted them fo far.
Without recurring to a period fo remote, we are
fumciently convinced, that if we were determined to
believe nothing of what we hear from others, or read
Vol. II. B in
2 MISTAKES IN THE
in their writings, we fhould be in a ftate of almofl
total ignorance. It is very far, however, from being
our duty to believe every thing that is faid, or that
we read. We ought conftantly to employ Our dis-
cerning faculties, not only with refpect to truths of
the third ciafs, but like wife of the two others.
We are fo liable to fuffer ourfelves to be dazzled
by the fenfes, and to nliftake in our reafonings, that
the very fources laid open by the Creator for the
difcovery of truth, very frequently plunge us into
error. Notions of the third clafs, therefore, ought
not," in reafon, to fall under fufpicion, any more than
fuch as belong to the other two. We ought, there-
fore, to be equally on our guard againft deception,
whatever be the clafs to which the notion belongs ;
for we find as many inftances of error in the firft
and fecond clafTes as in the third. The fame thing
holds with regard to the certainty of the particular
articles of knowledge which thefe three fources fup-
ply ; and it cannot be affirmed that the truths of
any one order have a furer foundation than thofe of
another. Each clafs is liable to errors, by which we
may be milled ; but there are likewife precautions
which, carefully obferved, furniih us with nearly
the fame degree of conviction. I do not know
whether you are more thoroughly convinced of this
truth, that two triangles which have the fame bafe,
and the fame height, are equal to one another, than
of this, that the Ruffians have been at Berlin ;
though the former is founded on a chain of accurate
rea foiling,
KNOWLEDGE OF TRUTH. g
)reafoning, whereas the latter depends entirely on the
Veracity of your informer*
Refpe&ing the truths, therefore, of each of thefe
clafles, we muft reft fatisfied with fuch proofs as
correfpond to their nature j and it would be ridicu-
lous to infift upon a geometrical demonftration of
the truths of experience, or of hiftory. This is ufu-
ally the fault of thofe who make a bad ufe of their
penetration in intellectual truths, to require mathe-
matical demonftration, in proof of all the truths of
religion, a great part of which belongs to the third
clafs.
There are perfons determined to believe and ad-
mit nothing but what they fee and touch 5 what-
ever you would prove to them by reafoning, be it
ever fo folid, they are difpofed to fufpeft, unlefs you
place it before their eyes. Chymifts, anatomifts, v
and natural philofophers, who employ themfelves
wholly in making experiments, are moft chargeable
with this fault. Every thing that the one cannot
melt in his crucible, or the other dkTect with his
fcalpel, they reject as unfounded. To no purpofe
you would fpeak to them of the qualities and nature
of the foul j they admit nothing but what ftrikes
the fenfes.
Thus, the particular kind of ftudy to which every
one is addicted, has fuch a powerful influence on his
manner of thinking, that the natural philofopher
and chymift will have nothing but experiments, and
the geometrician and logician nothing but argu=>
ments j which conftitute, however, proofs entirely
B 2 different,
4 MISTAKES, &C.
different, the one attached to the firft clafs, the other
to the fecond, which ought always to be carefully
diilinguiihed, according to the nature of the objects.
But can it be pofiible that perfons fhould exift,
who, wholly abforbed in purfuits pertaining to the
third clafs, call only for proofs derived from that
fource ? I have known fome of this defcription, who,
totally devoted to the fludy of hiftory and antiquity,
would admit nothing as true, but what you could
prove by hiftory, or the authority of fome ancient
author. They perfectly agree with you, refpecting
the truth of the proportions of Euclid, but merely
on the authority of that author, without paying any
attention to the demonftrations by which he fup-
ports them ; they even imagine that the contrary
of thefe proportions might be true, if the ancient
geometricians had thought proper to maintain it.
This is a fource of error which retards many in
the purfuit of truth j but we find it rather among
the learned, than among thofe who are beginning to
apply themfelves to the ftudy of the fciences. We
ought to have no _ predilection in favour of any one
of the three fpecies of proofs which each clafs re-
quires ; and provided they are fufficient, in their
kind, we are bound to admit them.
/ have fcen or felt, is the proof of the firft clafs.
I can demonftrate it, is that of the fecond ; we like-
wife fay, / know it is fo. Finally, / receive it on the
tejiimony of perfons worthy of credit, or / believe it on
folid grounds, is the proof of the third clafs.
Aftb April, 1761,
LETTER
OBJECTION OF THE PYRRHONISTS. $
LETTER II.
Firji Clafs of known Truths, Convicllon that Things
exifi externally correfponding to the Ideas rcprefented
by the Senfes. Objection of the Pyrrhoriifis. Reply.
TI7E include in the firft clafs of known truths,
* * thofe which we acquire immediately by means
of the fenfes. I have already remarked, that they
not only fupply the foul with certain reprefentations
relative to the changes produced in a part of the
brain ; but that they excite there a conviction of the
real exiftence of things external, correfponding to
the ideas which the fenfes prefent to us.
The foul is frequently compared to a man {hut up
in a dark room, in which the images of external ob-
jects are reprefented on the wall by means of a glafs.
This comparifon is tolerably juft, as far as it refpecfcs
the man looking at the images on the wall : for this
act is fuhicientiy iimilar to that of the foul, contem-
plating the impreffions made in the brain ; but the
comparifon appears to me extremely defective, as far
as it refpects the conviction, that the objects, which
occafton thefe images, really exift.
The man in the dark room will immediately fuf*
peel the exiftence of thefe objects j and, if he has no
doubt about the matter, it is becaufe he has been out
of doors, and has feen them ; befides this, knowing
the nature of his glafs, he is allured, that nothing can
be reprefented on the wall but the images of the ob-
jects which are without the chamber before the glafs.
B 3 But
6 OBJECTION OF THE PYRRHONISTS.
But this is not the cafe with the foul ; it has never
quitted its place of relidence to contemplate the ob-
jects themfelves : and it knows ftill lefs the conftruc-
tion of the fenfitive organs, and the nerves which
terminate in the brain. It is, neverthelefs, much
more powerfully convinced of the real exiftence of
objects, than our man in the dark room poffibly can
be. I am apprehenfive of no objection on the fubject,
the thing being too clear of itfelf to admit any, though
we do not know the true foundation of it. No one
ever entertained any doubt about it, except certain
viiionaries, who have bewildered themfelves in their,
own reveries. Though they fay, that they doubt the
exiftence of external objects, they entertain no fuch
doubt in fact. ; for why would they have affirmed it,
unlefs they had believed the exiftence of other men,
to whom they wifhed to communicate their extrava-
gant opinions ?
This conviction, refpecting the exiftence of the,
things whofe images the fenfes reprefent, appears not
only in men of every age and condition, but likewife
in all animals. The dog which barks at me has no
doubt of my exiftence, though his foul perceives but
a flight image of my perfon. Hence I conclude, that
this conviction is eiTentially connected with our fen-
fationsa and that the truths which the fenfes, convey
to us 3 are as well founded as the moil undoubted
truths of geometry.
Without this conviction no human fociety could
fubfift, for we.fhould be continually falling into the
greateft ahfurclities, and the groffeft contradictions.
Were
OBJECTION OF THE PYRRHONISTS. 7
Were the peafantry to dream of doubting about
the exiftence of their bailiff, or foldiers about that
of their officers, into what confufion mould we be
plunged! fuch abfurdities are entertained only by
philofophers ; any other giving himfelf up to them,
would be confidered as having loft his reafon. Let
us, then, acknowledge this convictiorf as one of the
principal laws of nature, and that it is complete,
though we are abfolutely ignorant of its true reafons,
and very far from being able to explain them in an
intelligible manner.
However important this reflection may be, it is
by no means, however, exempted from difficulties ;
but were they ever fo great, and though it might be
impoffible for us to folve them, they do no$ in the
fmalleft degree affect, the truth which I have juft
eftablifhed, and- which we ought to confider as the
molt folid foundation of human knowledge.
It muft be allowed, that our fenfes fometimes de-
ceive us ; and hence it is that thofe fubtile philofo-
phers, who value themfelves on doubting o£ every
thing, deduce the confequence, that we ought never
to depend on Our fenfes. I have perhaps often er
than once met an unknown perfon in the flreet,
whom I miftook for an acquaintance : as I was de-
ceived in that inftance, nothing prevents my being
always deceived ; and I am, therefore, never allured,
that the perfon to whom I fpeak is in reality the one
I imagine.
Were I to go to Magdeburg, and to prefent my- ■
felf to your Highiiefs, I ought always to be appre-
B 4 heniive
8 ANOTHER OBJECTION OF
henfive of grofsly miitaking : nay, perhaps, I mould
not be at Magdeburg, for there are initances of a
man's fometimes taking one city for another. It is
even poffible I may never have had the happinefs of
feeing you, but was always under the power of de-
lufion, when I thought myfelf to be enjoying that
felicity.
Such are the natural confequences refulting from
the fentiments of certain philofophers ; and you muft
be abundantly fenfible, that ^hey not only lead to
manifeft abfurdity, but have a tendency to diffolve
all the bands of fociety,
7 th April, 1 76 1,
LETTER III.
Another Objection of the Pyrrhonifts againjl the Certainty
of Truths perceived by the Senfes. Reply ; and Pre-
cautions for attaining Ajfurance of fenfible Truths.
fT^HQUGrH the objection raifed againft the cer-
-"- tainty of truths perceived by the fenfes, of
which I have been fpe'aking, may appear mfficiently
powerful, attempts have been made to give it addi-
tional fupport from the well-known maxim, that
we ought never to truft him who has once deceived
us. A fingle example, therefore, of miftake in the.
fenfes, is fufficient to deftroy all their credit. If this
objection is well-founded, it muft be admitted, that
human fociety is, of courfe, completely fubverted.
By way of reply, I remark, that the two other
fources
THE PYRRHONISTS. 9
iburces of knowledge are fubject to difficulties of a
fimilar nature, nay perhaps ftill more formidable.
How often are our reafonings erroneous ? I venture
to affirm, that we are much more frequently de-
ceived by thefe, than by our fenfes. But does it
follow, that our reafonings are always fallacious, and
that we can have no dependance on any truth difco-
vered to us by the underilanding? It muil be a mat-
ter of doubt, then, whether two and two make four,
or whether the three angles of a triangle be equal to
two right angles j it would even be ridiculous to pre-
tend that this mould pafs for truth. Though, there-
fore, men may have frequently reafoned inconclu-
lively, it would be moil abfurd to infer, that there
are not many intellectual truths, of which we have
the moil complete conviction.
The fame remark applies to the third fource of
human knowledge, which is unqueilionably the moil
fubject to error. How often have we been deceived
by a groundlefs , rumour, or falfe report reflecting
certain events ? And who would be fo weak as to
believe all that gazetteers and hiftorians have writ-
ten ? At the fame time, whoever ihould think of
maintaining that every thing related or written by
others is falfe, would undoubtedly fall into greater
abfurditiesjthan the perfon who believed every thing.
Accordingly, notwithstanding fo many groundlefs
reports and falfe teftimonies, we are perfectly allured
of the truth of numberlefs facts, of which we have
no evidence but teflimony.
There are certain characters which enable us to
diflinguiih
SO ANOTHER OBJECTION OF
diftinguifh truth, and each of the three fources has
characters peculiar to itfelf. When my eyes have
deceived me, in miftaking one man for another, I
prefently difcovered my error ; it is evident, there-
fore, that precautions may be ufed for the preven-
tion of error. If there were not, it would be im-
pollible ever to perceive that we had been deceived.
Thofe, then, who maintain that we fo often deceive
ourfelves, are obliged to admit, that it is poffible for
us to perceive we have been deceived, or they muft
acknowledge that they themfelves are deceived when
they charge us with error.
It is remarkable, that truth is fo we'll eftablifhed,
that the moft violent propenfity to doubt of every
thing, muft come to this, in fpite of itfelf. There-
fore, as logick prefcribes rules for juft reafoning, the
obfervance of which will feture us from error, where
intellectual truth is concerned; there are likewife
certain rules, as well for the iirft fource, that of our
fenfes, as for the third, that of belief.
The rules of the firfl are fo natural to us, that all
men, the moft ftupid not excepted, underftand and
practife them much better than the greateft fcholars
are able to defcribe them. Though it may be eafy
fometimes to confound a clown, yet when the hail
deftroys his crop, or the thunder breaks upon his
cottage, the moft ingenious phiiofopher will never
perfuade him that it was a mere illufion ; and every
man of fenfe muft admit that the country-fellow is
in the right, and that he is not always the dupe of
the fallaciouftiefs of his fenfes. The phiiofopher may
i be
THE PYRRHONISTS. II
be able, perhaps, to perplex him to fuch a degree
that he fhall be unable to reply, but he will inwardly
treat all the line reafonings, which attempted to con-
found him, with the utmoil fcorn. The argument,
that the fenfes fometimes deceive us, will make but
a very flight impreflion on his mind ; and when he
is told, with the greatest eloquence, that every thing
the fenfes reprefent to us has no more reality than the
vifions of the night, it will only provoke laughter.
But if the clown mould pretend to play the phi-
lofopher, in his turn, and maintain thai the bailiff is
a mere phantom, and that all who confider him as
fomething real, and fubmit to his authority, are
fools ; this fublime philofophy would be in a mo-
ment overturned, and the leader of the feci foon
made to feel, to his coft, the force of the proofs which
the bailiff could give him of the reality of his ex-
igence.
You muft: be perfectly fatisfied, then, that there
are certain characters which deftroy every ihadow
of doubt refpecting the reality and truth of what we
know by the fenfes ; and thefe fame characters are fo
Weil known, and fo ftrongly imprefled on our minds,
that we are never deceived when we employ the
precautions neceffary to that effect. But it is ex-
tremely difficult to make an exact enumeration of
thefe characters, and to explain their nature. We
commonly lay, that the fenfitive organs ought to be
in a good natural ilate; that the air ought not to, be
obfeured by a fog; finally, that we muft employ a
fufScient degree of attention, and endeavour, above
all
12 DEMONSTRATIVE, PHYSICAL,
all things, to examine the fame object by two or
more of our fenfes at once. But I am firmly per-
fuaded, that every one knows, and puts in practice,
rules much more folid than any which could be pre-*
fcribed to him.
I lib April, 1 76 1.
LETTER IV.
Of demonjlrative, phyfical, and particularly of moral,
Certainty.
k 1 *HERE are, therefore, three fpecies of know-
-*■ ledge, which we muft confider as equally cer-
tain, provided we employ the precautions necefTary
to fecure us againft error. And hence, likewife, re-
fult three fpecies of certainty.
The firft is called phyfical certainty. When I am
convinced of the truth of any thing, becaufe I my-
felf have feen it, I have a phyfical certainty of it ;
and, if I am afked the reafon, I anfwer, that my own
fenfes give me full affurance of it, and that I am, or
have been, an eye-witnefs of it. It is thus I know,
that Auftrians have been at Berlin, and that fome
of them committed great irregularities there. I
know, in the fame manner, that fire confumes all
combuflible fubftances; for I myfelf have feen it, and
I have a phyfical certainty of its truth.
The certainty which we acquire by a procefs of
reafoning, is called logical or demonfirative certainty,
becaufe we are convinced of its truth by demonfrra-
tion.
AND MORAL CERTAINTY. 1 3
t:on. The truths of geometry may here be produced
as examples, and it is logical certainty which gives
us the affurance of them.
Finally, the certainty which we have of the truth
of what we know only by the report of others, is
called moral certainty, becaufe it is founded on the
credibility of the perfons who make the report. Thus,
you have only a moral certainty that the Ruffians
have been at Berlin, and the fame thing applies to
all hiftorical facts. We know with a moral certainty,
that there was formerly at Rome a Julius Caefar, an
Auguftus, a Nero, &c. and the teftimonies refpecting
thefe are fo authentic, that we are as fully convinced
of them, as of the truths which we difcover by our
fenfes, or by a chain of fair reafoning.
We mult take care, however, not to confound
thefe three fpecies of certainty, phyfiqal, logical, and
moral, each of which is of a nature totally different
from the others. I propofe to treat of each fepa-
rately ; and mall begin with a more particular expla-
nation of moral certainty, which is the third fpecies.
It is to be attentively remarked, that this third
fource divides into two branches, according as others
fimply relate what they themfelves have feen, or made
full proof of by their fenfes, or as they communicate
to us, together with thefe, their reflections and rea-
fonings upon them. We might add ftill a third
branch, when they relate what they have heard from
others.
As to this third branch, it is generally allowed to
be very liable to error, and that a witnefs is to be
believed
14 DEMONSTRATIVE, PHYSICAL,
believed only reflecting what he himfelf has feen o£
experienced. Accordingly, in courts of juftice, when
witnefies are examined, great care is taken to dif-
tinguiih, in their declarations, what they themfelves
have feen and experienced, from what they fre-
quently add of their reflections and reafonings upon
it. Strefs is laid only on what they themfelves have
feen or experienced; but their reflections, and the
conclulions which they draw, however well founded
they may otherwife be, are entirely fet alide. The
fame maxim is obferved with refpect to hiftorians,
and we wifh them to relate only what they them-
felves have witnefTed, without purfuing the ^reflec-
tions which they fo frequently annex, though thefe
may be a great ornament to hiftory. Thus we have
a greater dependance on the truth of what others
have experienced by their own fenfes, than on what
they have difcovered by purfuing their meditations.
Every one wifhes to be mafter of his own judgment,
and tinlefs he himfelf feels the foundation and the
demonftration, he is not perfuaded.
Euclid would in vain have announced to us the
molt important truths of geometry; we fhould ne-
ver have believed him on his word, but have infiftec^
on profecuting the demonftration ftep by ftep our-
felves. If I were to tell you, that I had feen fuch
or fuch a thing, fuppofing my report faithful, you
would without hefitation give credit to it ; nay I
mould be very much mortified if you were to fuf-
pect me of falfhood. But when I inform you, that
in a right-angled triangle, the fquares dcfcribcd on
the
AMD MORAL CERTAINTY. 1$
the two fmaller fides are together equal to the fquare
of the greater fide, I do not wifh to be believed on
my word, though I am as much convinced of it, as
it is poffible to be of any thing ; and though I could
allege, to the fame purpofe, the authority of the
greateft geniufes who have had the fame conviction,
I mould rather wifh you to difcredit my alfertion,
and to withhold your affent, till you yourfelf com-
prehended the folidity of the reafonings on which
the demonftration is founded.
It does not follow, however, that phyfical cer-
tainty, or that which the fenfes fupply, is greater
than logical certainty, founded on reafoning; but,
whenever a truth of this fpecies prefents itfelf, it is
proper that the mind fhould give clofe application to
it, and become mafter of the demonftration. This
is the bell method of cultivating the fciences, and of
carrying them to the higheft degree of perfection.
The truths ©f the fenfes, and of hiftory, greatly
multiply the particulars of human knowledge; but
the faculties of the mind are put in action only by
reflection or reafoning.
We never flop at the fimple evidence of the fenfes,
or the fads related by others; but always follow
them up and blend them with reflections of our
own : we infenfibly fupply what feems deficient, by
the addition of caufes and motives, and the deduc-
tion of confequences. It is extremely difficult, for
this reafon, in courts of juftice, to procure fimple,
unblended teftimony, fuch as contains what the wit-
nefs actually faw and felt, and no more; for witnefles
ever
l6 THE SENSES CONTRIBUTE TO
ever will be mingling their own reflections, without
perceiving that they are doing fo*
l^tb April, 1 76 1.
LETTER V.
Remarks that the Senfes contribute to the Increafe of
Knowledge ; and Precautions for acquiring the Cer~
. tainty of Hijiorical Truths,
'"TPHE knowledge fupplied by our fenfes is un-
-** doubtedly the earlieft which we acquire, and
upon this the foul founds the thoughts and reflec-
tions which difcover to it a great variety of intel*
tactual truths. In order the better to comprehend
how the fenfes contribute to the advancement of
knowledge, I begin with remarking, that the fenfes
act only on individual things, which actually exifl:
under circumftances determined or limited on all
fides.
Let us fuppofe a man fuddenly placed in the world,
poiTelfed of all his faculties, but entirely deftitute of
experience; let a Hone be put in his hand, let him
then open that hand, and obferve that the ftone falls.
This is an experiment limited on all fides, which
gives him no information, except that this ftone be-
ing in the left hand, for example, and dropped, falls
to the ground ; he is by no means abfolutely certain
that the fame effect would enfue, were he to take
another ftone, or the fame ftone with his right hand.
It
THE INCREASE OF KNOWLEDGE. 1J
Xt is ftill uncertain whether this ftone, under the
fame circumftances, would again fall, or whether it
would have fallen, had it been taken up an. hour
fooner. This experiment alone gives him no light
refpecting thefe particulars.
The man in queftion takes another ftone, and ob-
serves that it falls likewife, whether dropped from
the right hand or from the left ; he repeats the ex-
periment with a third and a fourth ftone, and uni-
formly obferves the fame effect. He hence concludes
that ftones have the property of falling when drop-
ped, or when that which fupports them is with-
drawn.
Here then is an article of knowledge which the
. man has derived from the experiments which he has
made. He is very far from having made trial of
every ftone, or, fuppofing him to have done fo, what
certainty has he that the fame thing would happen
\ at all times? He knows nothing as to this, except
what concerns the particular moments when he made
the experiments ; and what afliirance has he that the
fame effect would take place in the hands of another
. man ? Might he not think, that this quality of
making ftones fall was attached to his hands exclu-
sively? A thoufand other doubts might ftill be
formed on the fubjecl. ,
I have never, for example, made trial of the ftones
which compofe the cathedral church of Magdeburg,
and yet I have not the leaft doubt, that all of them
without exception are heavy, and that each of them
would fall as foon as detached from the building.
Vol. II. C I even
l3 THE SENSES GONTRIBUtfi tO
I even imagine that experience has fupplied me with
this knowledge, though I have never tried any one
of thofe (tones*
This example is fufficient to fhew, how experi-
ments made on individual obje&s . only, have led
mankind to the knowledge of univerfal proportions ;
but it mull be admitted, that the underftanding and
the other faculties of the foul interfere in a manner
which it would be extremely difficult dearly to un-
fold j and if we were determined to be over fcrupu-
lous about every circumftance, no progrefs in fcience
could be made, for we fhould be Hopped fhort at
every ftep.
It mull: be allowed, that the vulgar difcover, in
this refpecl, much more good fenfe than thofe fcru-
pulous philofophers, who are obftinately determined
to doubt of every thing. It is neceffary, at the fame
time, to be on our guard againft falling into the op-
polite extreme, by negle&ing to employ the neceffary
precautions.
The three fources from which our knowledge is
, derived, require all of them certain precautions,
which muft be carefully obferved, in order to ac-
quire afhirance of the truth \ but it is poflible, in
each, to carry matters too far, and it is always pro-
per to fleer a middle courfe.
The third fource clearly proves this. It would
undoubtedly be extreme folly to believe every thing
that is told us ; but exceflive diftruft would be no
lefs blame-worthy. He who is determined to doubt
of every thing, will never want a pretence : when a
man
THE INCREASE OF KNOWLEDGE. jg
man fays, or writes, that he has feen fuch or fuch
an action, we may fay at once, that is not true, and
that the man takes amufement in relating things
which may excite furprize; and if his veracity is
beyond fufpicion, it might be faid, that he did not
fee clearly, that his eyes were dazzled; and examples
are to be found in abundance of perfons deceiving
themfelves, falfely imagining they faw what they did
not. The rules prefcribed, in this refpect, lofe all
their weight when you have to do with a wrangler.
Ufually, in order to be afcertained of the truth of a
recital or hiftory, it is required, that the author fhould
have been himfelf a witnefs of what he relates, and
that he mould have no intereft in relating it diffe-
rently from the truth. If afterwards two or more
perfons relate the fame thing, with the fame circum-
ftances, k is juftly coniidered as a ftrong confirma-
tion. Sometimes, however, a coincidence carried
to extreme minutenefs becomes fufpicious. For two
perfons obferving the fame incident, fee it in diffe-
rent points of view, and the one will always difcern
certain little circumftances which the other muit have
overlooked. A flight difference in two feveral ac-
counts of the fame event, rather eflablifhes than in-
validates the truth of it.
But it is always extremely difficult to reafon on
the firft principles of our knowledge, and to attempt
an explanation of the mechanifm and of the moving
powers which the foul employs. It would be glo-
rious to fucceed in fuch an attempt, as it would elu-
cidate a great variety of important points refpecting
the nature of the foul and its operations. But- we
C 2 . feem
20 WHE < HE& THE ESSENCE. OF
feerri deftined rather to make ufe of our faculties,
than to trace their nature through all its, depths.
iStb Apr'ily 1 76 1.
-~j»»-;c"?;
LETTER VL
Whether the Effence of Bodies be known by us*
X FTER fo many reflections on the nature and
-*- -*■ faculties of the foul, you will not, perhaps, be
difpleafed to return to the confideration of body, the
principal properties of which I have already endea-
voured to explain.
I have remarked that the nature of body necef-
farily contains three things, extenjion, impenetrability ',
and inertia ; fo that a being, in which thefe three
properties do not meet at once, cannot be admitted
into the clafs of bodies j and reciprocally, when they
are united in any one being, no one will hefitate to
acknowledge it for a body.
In thefe three things, then, we are warranted to
■conftitute the effence of body, though there are many
philofophers who pretend that the effence of bodies
is wholly unknown to us. This is not only the
• opinion of the Pyrrhonifts, who doubt of every
thing ; but there are other feels likewife, who main-
tain, that the effence of all things is abfolutely un-
known : and no doubt, in certain refpecls they have
truth on their fide : this is but too certain as to all
the individual beings which exift.
You will eafily comprehend, that it would be the
height of abfurdity were I to pretend fo much as to
know
BODIES BE KNOWN BY US. 21
know the effence of the pen which I employ in writ-
ing this letter. If I knew the effence of this pen, (I
fpeak not of pens in general, but of that one only
now between my fingers, which is an individual beings
as it is called in metaphyfics, and which is diilin-
guifhed from all the other pens in the world ;) if I
knew, then, the effence of this individual pen, 1
mould be in a condition to diftinguiih it' from every
other, and it would be impoffible to change it with-
out my perceiving the change ; I muff know its na-
ture thoroughly, the number and the arrangement of
all the parts whereof it is compofed. But how far
am I from having iuch a knowledge ! Were I to rife
but for a moment, one of my children might eafily
change it, leaving another in its room, without my
perceiving the difference ; and were I even to put a
mark upon it, how eafily might that mark be coun-
terfeited on another pen ? And fuppoling this im-
poffible for my children, it muft always be admitted
as poffible for God ■ to make another pen fo limilar to
this, that I fhould be unable to difcern any difference.
It would be, however, another pen, really diftin-
guifhable from mine, and God would undoubtedly
know the difference of them ; in other words, God
perfectly knows the effence of both the one and the
other of thefe two pens : but as to me, who difcern
no difference, it is certain that the effence is altogether
beyond my knowledge.
The fame obfervation is applicable to all other in-
dividual things ; and it may be confidently main-
tained, that God alone can know the effence or na-
ture of each. It were impoffible to fix on any one
C 3 thing
22 WHETHER THE ESSENCE OP
thing really exifting, of which we could have a know-
ledge fo perfect, as to put us beyond the reach of
miftake : this is, if I may ufe the expreulon, the im-
prefs of the Creator on all created things, the nature
of which will ever remain a myftery to us.
It is undoubtedly certain, then, that we do not -
know the effence of individual things, or all the cha-
racters whereby each is diftinguiftied from every
other ; but the cafe is different with refpect to genera
•md /pedes: thefe are general notions which include
at once an infinite number of individual things.
They are not beings actually exifting, but notions
which we ourfelves form in our minds, when we
arrange a great many individual things in the fame
clafs, which we denominate a fpecies or genus, ac-
cording as the number of individual things which it
comprehends is greater or lefs.
And to return to the example of the pen, as there.
are an infinite number of things to each of which I
give the fame name, though they all differ one from
another ; the notion of pen is a general idea of which
we ourfelves are the creators, and which exifts only
in our own minds. This notion contains but the
common characters which conftitute the effence of
the general notion of a pen ; and this effence muff
be well known to us, as we are in a condition to
diftinguifh. ail the things which we call pens from
thofe which we do not comprehend under that ap-
pellation.
As foon as we remark in any thing certain cha-
racters, or certain qualities, we fay it is a pen ; and
we are in a condition to cliixinguifli it from ail other
things
BODIES BE KNOWN BY US. 23
things which are not pens, though we are very far
from being able to diftinguilh it from other pens.
The more general a notion is, the fewer it con-
tains of the characters which conftitute its effence,
and it is accordingly eafier alfo to difcover this
effence. We comprehend more eafily what is meant
by a tree, in general, than by the term cherry-tree,
pear-tree, or apple-tree ; that is, when we defcend to
the fpecies. When I fay, fuch an object, which I fee
in the garden is a tree, I run little rifK of being mif-
taken ; but it is extremely poiTible I might be wrong,
if 1 affirmed it was a cherry-tree. It follows then,
that I know much better the effence of tree, in ge-
neral, than of the fpecies : I mould not fo eafily con-
found a tree with a {tone, as a cherry-tree with a
plum-tree..
Now a notion, in general, extends infinitely far-
ther ; its effence accordingly comprehends only the
characters which are common to all beings bearing
the name of bodies. It is reduced, therefore, to a very
few particulars, as we muft exclude from it all the
characters which diftinguifh one body from another.
It is ridiculous then to pretend, with certain phi-
lofophers, that the effence of bodies, in general, is
unknown to us. If it were fo, we mould never be
in a condition to affirm with affurance, that fuch a
thing is a body, or it is not : and as it is impoffiblfe
we fhould be miftaken in this refpect, it necefiarily
follows, that we know fufficiently the nature or ef-
fence of body in general; Now this knowledge is
reduced to three articles, extenfion, impenetrability,
and inertia.
ai/4>,v75i76i. LETTER
24 THE TRUE NOTION OF EXTENSION,
LETTER VII.
The true Notion of Extenjion.
T HAVE already demonftrated, that the genera^
■*■ notion of body neceffarily comprehends thefe
three qualities, extenfion, impenetrability, and inertia,
without which no being can be ranked in the clafs of
bodies. Even the moil fcrupulous muft allow the
necefiity of thefe three qualities, in order to confti-
tute a body ; but the doubt with fonie is, Are thefe
three . characters fufiicient ? Perhaps, fay they, there
may be feveral other characters, which are equally
neceffary to the effence of body.
But I alk : were God to create a being divefted of
thefe other unknown characters, and that it polfeffed
only the three above mentioned, Would they hefi-
tate to give the name of body to fuch a being ? No,
affuredly ; for if they had the leatt doubt on the
fubjecl, they could not fay with certainty, that the
, ft ones in the ftreet are bodies, becaufe they are not
fure whether the pretended unknown characters are.
to be found in them or no.
Some imagine, that gravity is an effential property
of all bodies, as all thofe which we know are heavy;
but were God to divcft them of gravity, would they
therefore ceafe to be bodies ? Let them confider the
fyeavenly bodies, which do not fall downward ; as
muft be the cafe, if they were heavy as the bodies
which we touch, yet they give them the fame name.
And
THE TRUE NOTION OF EXTENSION. 25
And even on the fuppofition that all bodies were
heavy, it would not follow that gravity is a property
elfential to them, for a body would {till remain a
body, though its gravity were to.be deflroyed by a
miracle.
But this reafoning does not apply to the three ef-
fential properties above mentioned. Were God to
annihilate the extenfion of a body, it would certainly
be no longer a body ; and a body divefted of impe-
netrability would no longer be body ; it would be a
fpectre, a phantom : the fame holds as to inertia.
You know that extenfion is the proper object of
geometry, which confiders bodies only in fo far as
they are extended, abftractedly from impenetrability
and inertia ; the object of geometry, therefore, is a
notion much more general than that of body, as it
comprehends not only bodies, but all beings limply
extended without impenetrability, if any fuch there
be. Hence it follows, that ail the properties deduced
in geometry from the notion of extenfion mult like-
wife take place in bodies, in as much as they are ex-
tended ; for whatever is applicable to a more general
notion, to that of a tree, for example, mult likewife
be applicable to the notion of an oak, an afh, an elm,
&c. and this principle is even the foundation of all
the reafpnings in virtue of which we always affirm
and deny of the fpecies, and of individuals, every ,
thing that we affirm and deny of the genus.
There are however philofophers,particularlyamong
our contemporaries, who boldly deny, that the pro-
perties applicable to extenfion, in general, that is,
according
Z6 THE TltOS NOTION OF EXTENSION.
according as we confider them in geometry, take
place in bodies really exifting. They allege that geo-
metrical extenfion is an abftract. being, from the pro-
per ties of which it is impoffible to draw any conclu-
fion, with refped to real objects : thus, when I have
demonftrated that the three angles of a triangle are
together equal to two right angles, this is a property
belonging only to an abftract. triangle, and not at all
to one really exifting.
But thefe philofophers are not aware of the per-
plexing confequences which naturally refult from
the difference which they eftablifh between objects
formed by abitraction, and real objects ; and if it
were not permitted to conclude from the firft to the
laft, no conclusion, and no reafoning whatever could
fubfift, as we always conclude from general notions
to particular.
Now all general notions are as much abftract beings
as geometrical extenfion ; and a tree, in general, or
the general notion of trees, is formed only by ab-
ftraction, and no more exifts out of our mind than
geometrical extenfion does. The notion of man in
general is of the fame kind, and man in general no
where exifts : all men who exift are individual beings,
and correfpond to individual notions. The general
idea which comprehends all, is formed only by ab-
ftraciion.
The fault which thefe philofophers are ever find-
ing with geometricians, for employing themfelves
about abstractions merely, is therefore groundlefs, as
all other fciences principally turn on general notions,
2 which
DIVISIBILITY, &C. 27
which are no more real than the objects of geometry.
The patient, in general, whom the phyfician has in
view, and the idea of whom contains all patients
really exifting, is only an abftract idea ; nay the very
merit of each fcience is fo much the greater, as it ex-
tends to notions more general, that is to fay, more
abftract.
I fhall endeavour, by next poft, to point out the
tendency of the cenfures pronounced by thefe phi-
lofophers upon geometricians ; and the reafons why
they are unwilling that we Ihould afcribe to real,
extended beings, that is, to exifting bodies, the pro-
perties applicable to extenlion in general, or to ab-
ft rafted extenfion. They are afraid left their meta*
phyfical principles ihould fuffer in the caufe.
2 5/6 April t 1 761.
LETTER VIII.
Dlvifibility of Exterfwn in infinitum.
THE controverfy between modern philofophers
and geometricians to which I have alluded,
turns on the dlvifibility of body. This property is
undoubtedly founded on extenlion, and it is only in
fo far as bodies are extended that they are divilible,
and capable of being reduced to parts.
You will recollect that in geometry it is always
poffible to divide a line, however fmall, into two
equal parts. We are likewife, by that fcience, in-
ftructed
28 DIVISIBILITY OF
ftracted in the method of dividing a fmall line, as
a i, into any number of equal parts at pleafure, and
the conftruc&on of this diviiion is there demonftrated
beyond the poiTibility of doubting its accuracy.
You have only to draw (plate II. Jig. 2-5.) a line
A I parallel to a /of any length, and at any diftance
you pleafe, and to divide it into as many equal parts
AB, BC, CD, DE, &c. as the fmall line given is to
have divisions, fay eight. Draw afterwards,through
the extremities A, a, and I, i, the ftraight lines A a
O, I i O, till they meet in the point O ; and from O
draw toward the points of divifion B, C, D, E, &c.
the ftraight lines OB, QC, OD, OE, &c. which mail
likewife cut the fmall line ai into eight equal parts.
This operation may be performed, however fmall
the given line ai, and however great the number of
parts into which you propofe to divide it. True it
is, that in execution we are not permitted to go too
far ; the lines which we draw always have fome
breadth, whereby they are at length confounded, as.
may be feen in the figure near the point O ; but the
queftion is not what may be poiiible for us to execute,
but what is poiiible in itfelf. Now in geometry lines
have no breadth, and confequently can never be con-
founded. Hence it follows that fuch divifion is il-
limitable.
, If it is once admitted that a line may be divided
into a thoufand parts, by dividing each part into two
it will be divifible into two thoufand parts, and for
the 'fame reafon into four thoufand, and into eight
thoufand, without ever arriving at parts in divifible.
However
EXTENSION IN INFINITUM. 29
However fmall a line may be fuppofed, it is ftill di-
vifible into halves, and each half again into two, and
each of thefe again in like manner, and fo on to in*
finity.
What I have faid of a line is eafily applicable to a
furface, and, with greater ffcrength of reafoning, to a
folid endowed with three dimenfions, length, breadth,
and thicknefs. Hence it is affirmed that all exten-
fion is divifible to infinity, and this property is deno-
minated divifibility in infinitum.
Whoever is difpofed to deny this property of ex-
tenfion, is under the necefiity of maintaining, that it
is poillble to arrive at laft at parts fo minute as to be
unfufceptible of any farther divifion, becaufe they
ceafed to have any extenfion. Neverthelefs all thefe
particles taken together muft reproduce the whole,
by the divifion of which you acquired them ; and as
the quantity of each would be a nothing or cypher o,
a combination of cyphers would produce quantity,
which is manifeftly abfurd. For you know perfectly
well, that in arithmetic, two or more cyphers joined
never produce any thing.
This opinion that in the divifion of extenfion, or
of any quantity whatever, we may come at laft to
particles fo minute as to be no longer divifible, be-
caufe they are fo fmall, or becaufe quantity no longer
exifts, is, therefore, a pofition abfolutely untenable.
In order to render the abfurdity of it more fen-
fible, let us fuppofe a line of an inch long, divided into
a thoufand parts, and that thefe parts are fo fmall as
to
$0 DIVISIBILITY, &C.
to admit of no farther divifion ; each part, then,
would no longer have any length, for if it had any,
it would be ftill divifible. Each particle, then, would
of confequence be a nothing. But if thefe thouiand
particles together conftituted the length, of an inch,
the thoufandth part of an inch would, ofconfequence,
be a nothing ; which is equally abfurd with main-
taining, that the half of t any quantity whatever is
nothing. And if it be abfurd to affirm, that the half
of any quantity is nothing, it is equally fo to affirm,
that the half of a half, or that the fourth part of the
fame quantity, is nothing ; and what mufl be granted
as to the fourth, muft likewife be granted with re-
fpecl to the thoufandth, and the millionth part. Fi-
nally, however far you may have already carried, in
imagination, the divifion of an inch, it is always
poffible to carry it ftill farther ; and never will you
be able to carry on your fubdivifion fo far, as that
the laft parts mall be abfolutely indivifible. Thefe
parts will undoubtedly always become fmaller, and
their magnitude will approach nearer and nearer to o,
but can never reach it.
The geometrician, therefore, is warranted in affirm-
ing, that every magnitude is divifible to infinity ;
and that you cannot proceed fo far in your divifion,
as that all farther divifion fhall be impoiTible. But
it is always neceffary to diftinguifh between what is
poffible in itfelf, and what we are in a condition to
perform. Our execution is indeed extremely limited.
After having, for example, divided an inch into a
thoufand
WHETHES. TtllS DIVISIBILITY, &C. $t
thoufand parts, thefe parts are fo fmall as to efcape
our fenfes, and a farther divifion would to us, no
doubt, be impofiible.
But you have only to look at this thoufandth part
of an inch through a good microfcope, which mag-
nifies, for example, a thoufand times, and each par-
ticle, will appear as large as an inch to the naked eye;
and you will be convinced of the poflibility of di-
viding each of thefe particles again into a thoufand
parts : the fame reafoning may always be carried for-
ward, without limit and without end.
It is therefore an indubitable truth, that all mag-
nitude is divifible in infinitum, and that this takes
place not only with refpect to extenfion, which is
the object of geometry, but like wife with refpecl to
every other fpecies of quantity, fuch as time and
number.
%%th Aprily 1761.
LETTER IX.
Whether this Dlvifibllity in infinitum takes place in
exifting Bodies?
IT is, then, a completely eftablifhed truth, that ex-
tenfion is divifible to infinity, and that it is inv
poilible to conceive parts fo fmall as to be unfufcep-
tible of farther divifion. Philofophers accordingly
do not impugn this truth itfelf, but deny that it
takes place in exifting bodies. They allege, that ex-
tenfion, the divisibility of which to infinity has been
demon-
32 WHETHER THIS DIVISIBILITY TAKES
dernonftrated, is merely a chimerical object, formed
by abftraction ; and that fimple extenfion, as confi*
dered in geometry, can have no real exiftence.
Here they are in the right ; and extenfion is un-
doubtedly a general idea, formed in the fame man-
ner as that of man, or of tree in general, by abftrac-
tion; and as man or tree in general exifts not, no
more does extenfion in general exiit. You are per-
fectly feniible, that individual beings alone exift, and
that general notions are to be found only in the
mind; but it cannot therefore be maintained that
thefe general notions are chimerical; they contain,
on the contrary, -the foundation of all our know-
ledge.
Whatever applies to a general notion, and all the
properties attached to it, of neceflity take place in
all the individuals comprehended under that general
notion. When it is affirmed that the general notion
of man contains an underftanding and a will, it is
undoubtedly meant, that every individual man is
endowed with thofe faculties. And how many pro-
perties do thefe very philofophers boaft of having
dernonftrated as belonging to fubftance in general,
which is furely an idea as abftracT: as that of exten-
fion; and yet they maintain, that all thefe properties
apply to all individual fubftances, which are all ex-
tended. If, in effect, fuch a fubftance had not thefe
properties, it would be falfe that they belonged to
fubftance in general.
If then bodies, which infallibly are extended be-
ings, or endowed with extenfion, were not divifible
to
PLACE IN EXISTING BODIES f 33
to infinity, it would be likewife falfe, that divifibi-
lity in infinitum is a property of extenfion. Now
thofe philofophers readily admit that this property
belongs to extenfion, but they infill that it cannot
take place in extended beings. This is the fame
thing with affirming, that the underfcanding and will
are indeed attributes of the notion of man in gene-
ral ; but that they can have no place in individual
men actually exifting.
Hence you will readily draw this conclusion ■: if
diviiibility in infinitum is a property of extenfion in
general, it muft of neceffity likewife belong to all
individual extended beings; or if real extended be-
ings are not divifible to infinity, it is falfe that divi-
fibility in infinitum can be a property of extenfion
in general.
It is impoffible to deny the one or the other of
thefe confequences without fubverting the moft fo-
lid principles of all knowledge ; and the philofophers
who refufe to admit divifibiiity in infinitum in real
' extended beings, ought as little to admit it with
refpecl: to extenfion in general; but as they grant
this laft, they fall into a glaring contradiction.
You need not to be furprized at this; it is a failing
from which the greateft men are not exempt. But
what is rather furprizing, thefe philofophers, in order
to get rid of their embarraffment, have thought pro-
. per to deny that body is extended. They fay, that
it is only an appearance of extenfion which is per-
ceived in bodies, but that real extenfion by no means
belongs to them.
Vol. II. D You
34 WHETHER THIS DIVISIBILITY, &C.
You fee clearly that this is merely a wretched cavil,
by which the principal, and the moft evident pro-
perty of body is denied. It is an extravagance nmi-
lar to that formerly imputed to the Epicurean phi-
lofophers, who maintained that every thing which
exifts in the univerfe is material, without even ex-
cepting the gods whofe exiftence they admitted. But
as they faw that thefe corporeal gods would be fub-
jected to the greateft difficulties, they invented a
fubterfuge fimilar to that of our modern philofo-
phers, alleging, That the gods had not bodies, but
as it were bodies, (auaft corpara,J and that -they had
not fenfes, but fenfes as it were; and fo of all the
members. The other philofophical feels of antiquity
made themfelves abundantly merry with thefe quafi-
corpora and quaji-fenfus ; and they would have equal
reafon, in modern times, to laugh at the quaji-exten-
fion which our philofophers afcribe to body; this
term quafi-extenfion feems perfectly well to exprefs that
appearance of extenfion, without being fo in reality.
Geometricians, if they meant to confound them,
have only to fay, that the objects whofe divifibility
in infinitum they have demonftrated, were likewife
only as it were extended, and that accordingly ail
bodies extended as it were, were neceffarily divifible
in infinitum. But nothing is to be gained with them ;
they are refolute to maintain the greateft abfurdities
rather than acknowledge a miftake. You muft have
remarked, that this is the character of almoft all
fcholars.
id May, 1 761,
LETTER
OF MONADS. 2S
LETTER X.
Of Monads.
TT7HEN we talk, in company, on philofophical
* * fubjects, the converfation ufually turns on
fuch articles as have excited violent difputes among
philofophers.
The diviiibility of body is one of them, refpe-fting
which the fentiments of the learned are greatly di-
vided. Some maintain, that this diviiibility goes on
to infinity, without the poffibility of ever arriving at
particles fo fmall as to be fufceptible of no farther
divifion. But others infill, that this divifion ex-
tends only to a certain point, and that you may come
at length to particles fo minute, that, having no
magnitude, they are no longer divisible. Thefe ul-
timate particles, which enter into the compofition of
bodies, they denominated^/? beings ', and monads.
There was a time when the difpute refpefting mo-
nads employed fuch general attention, and was con-
ducted with fo much warmth, that it forced its way
into company of every defcription, that of the guard-
room not excepted. There was fcarce a lady at court
who did not take a decided part in favour of mo-
nads or againft them. In a word, all converfation
was engroffed by monads, no other fubjecl: could
find admiflion.
• The Royal Academy of Berlin took up the con-
ttoverfy, and being accuftomed annually to propofe
Da a queflion
3^ OF MONADS.
a queftion for difcuflion, and to beftow a gold medal
of the value of fifty ducats on the perfon who in the
judgment of the Academy has given the moft inge-
nious folution, the queftion refpecting monads was ■
felected for the year 1748. A great variety of effays
on the fubject were accordingly produced. The
preiident, Mr. de Maupertuis, named a committee
to examine them, under the direction of the late
Count Dohna, great chamberlain to the queen ; who,
being an impartial judge, examined, with all imagi-
nable attention, the arguments adduced both for and
againft the exiftence of monads. Upon the whole,
it was found that thofe which went to the eftablilh-
ment of their exiftence were fo feeble, and fo chi-
merical, that they tended to the fubverfion of all the
principles of human knowledge. The queftion was,
therefore, determined in favour of the oppofite opi-
nion, and the prize adjudged to Mr. Jufti, whofe
piece was deemed the moft complete refutation of
the monadifts.
You may eafily imagine how violently this deci-
fion of the Academy muft irritate the partifans of
monads, at the head of whom ftood the celebrated
Mr. Wolff. His followers, who were then much
more numerous, and more formidable than at pre-
fent, exclaimed in high terms againft the partiality
and injuftice of the Academy; and their chief had
well nigh proceeded to launch the thunder of a phi-
lofophical anathema againft it. I do not now recol-
lect to whom we are indebted for the care of avert-
ing this difafter.
As
OF MONADS. 37
As this controverfy has made a great deal of noife,
you will not be difpleafed, undoubtedly, if 1 dwell a
little upon it. The whole is reduced to this fimple
queftion, Is body divifible to infinity? or, in other
words, Has the divifibility of bodies any bound, or
has it not? I have already remarked as to this, that
extenfion, geometrically conlidered, is on all hands
allowed to be divifible in infinitum; becaufe, how-
ever fin all a magnitude may be, it is poffible to con-
ceive the half of it, and aeain the half of that half,
and fo on to infinity.
This notion of exteniion is very abftract, as are
thofe of all genera, fuch as that of man, of horfe, of
tree, &c. as far as they are not applied to an indivi-
dual and determinate bein°\ Aerain, it is the,mofl
certain principle of all our knowledge, that whatever
can be truly affirmed of the genus, muft be true of
all the individuals comprehended under it. If there-
fore all bodies are extended, all the properties be-
longing to extenfion muft belong to each body iri
particular. Now all bodies are extended ; and ex-
tenfion is divifible to infinity; therefore everybody
muft be fo likewife. This is a fyllogifm of the beft
form; and as the firft propofition is indubitable, all
that remains, is to be allured that the fecond is true,
that is, whether it be true or not, that bodies are
extended.
The partifans of monads, iri maintaining their
opinion, are obliged to affirm, that bodies are not
extended, but have only an appearance of extenfion.
They imagine that by this they have fubverted the
D 3 argument
$8 OF MONADS.
argument adduced in fupport of the divifibility in in-
finitum. But if body is not extended, I fliould be
glad to know, from whence we derived the idea of
extenfion ; for, if body is not extended, nothing in
the world is, as fpirits are ftill lefs fo. Our idea of
exteniion, therefore, would be altogether imaginary
and chimerical.
Geometry would accordingly be a fpeculation en-
tirely ufelefs and illufory, and never could admit of
any application to things really exifting. In effect,
if no one thing is extended, to what purpofe inves-
tigate the properties of extenfion ? But as geometry
is, beyond contradiction, one of the moft ufeful of
fciences, its object cannot poffibly be a mere chi-
mera.
There is a neceffity,then,of admitting, that the ob-
ject of geometry is at leaft the fame apparent exten^
fion which thofe philofophers allow to body; but
this very object is divifible to infinity : therefore ex*
ifting beings, endowed with this apparent extenfion,
muft neceffarily be extended.
Finally, let thofe philofophers turn themfelves
which way foever they will in fupport of their mo-
nads, or thofe ultimate and minute particles, divefted
of all magnitude, of which, according to them, all
bodies are compofed, they ftill plunge into' difficul-
ties, out of which they cannot extricate themfelves.
They are right in faying, that it is a proof of dulnefs
to be incapable of relifhing their fublime doctrine ;
it may however be remarked, that here the greatefl
ftupidity is the moft fuccelsful.
stbMay, i76i. BETTER
REFLECTIONS ON DIVISIBILITY, &C. 39
LETTER XL
Reflettions on Div'ifibUity in infinitum, and on
Monads.
TN fpeaking of the divifibility of body, we muft
-*- carefully distinguish what is in our power, from
what is poffible in itfelf. In the Sirft fenfe, it cannot
be denied, that fuch a division of body as we are
capable of, muft be very limited.
By pounding a ftone we can eafily reduce it to
powder; and if it were poSiible to reckon all the
little grains which form that powder, their number
would undoubtedly be fo great, that it would be
matter of furprize, to have divided the ftone into fo
many parts. But thefe very grains will be almoft
indivisible with refpecl: to us, as no inftrument we
could employ will be able to lay hold of them. But
it cannot with truth be affirmed that they are indi-
vifible in themfelves. You have only to view them
with a good microfcope, and each will appear itfelf
a coniiderable ftone, on which are distinguishable a
great many points and inequalities j which demon-
strates the poffibility of a farther divifion, though
we are not in a condition to execute it. For where-
ever we can diftinguifh feveral points in any object,
it muft be divisible into fo many parts.
We fpeak not? therefore, of a division practicable
by our Strength and Skill, but of that which is pof-
fible in itfelf, and which the Divine Omnipotence is
able to accomplish.
D 4 It
40 REFLECTIONS ON DIVISIBILITY,
It is in this fenfe, accordingly, that philofophers
life the word ' divisibility;' fo that if there were a
ilone fo hard that no force could break it, it might
be without hefitation affirmed as divifible in its own
nature, as the moft brittle, of the fame magnitude.
And how many bodies are there on which we can-
not lay any hold, and of whofe divilibility we can
entertain not the frnalleft doubt? No one efcabts
that the moon is a divifible body, though he is in-
capable of detaching the frnalleft particle fror,
and the fimpie reafon for its divifibility, is its being
extended.
Wherever we remark extenfion, we are under the
neceffity of acknowledging divilibility, fo that divili-
bility is an infeparable property of extenfion. But
experience likewife demon Urates that the divifion of
bodies extends very far. I mail not infill at great
length on the inftance ufually produced of a ducat :
the artifan can beat it out into a leaf fo fine, as to
cover a very large furface, and the ducat may be di-
vided into as many parts as that furface is capable of
being divided. Our own body furnifhes an example
much more furprizing. Only confider the delicate
veins and nerves with which it is filled, and the fluids
which circulate through them. The fubtilty there
difcoverable far furpaffes imagination.
The frnalleft infects, fuch as are fcarcely vifible to
the naked eye, have all their members, and legs on
which they walk with amazing velocity. Hence we
fee that each limb has its mufcies compofed of a great
number of fibres \ that they have veins, and nerves,
and
AND ON MONADS. /f«
and a fluid flail much more fubtile which flows
through their whole extent.
On viewing with a good microfcope a fingle drop
of water, it has the appearance of a, fea ; we fee
thoufands of living creatures fwimming in it, each of
which is neceffarily compofed of an infinite number
of mufcular and nervous fibres, whofe marvellous
ftru&ure ought to excite our admiration. And
though thefe creatures may perhaps be the fmalleft
which we are capable of dilcovering by the help of
the microfcope, undoubtedly they are not the finalleft
which the Creator has produced. Animalcules pro-
bably exift as fmah relatively to them, as they are
relatively to us. And thefe after all are not yet the
finalleft, but may be followed by an infinity of new
claries, each of which contains creatures incomparably
fmaller than thole of the preceding clafs.
We ought in this to acknowledge the omnipotence
and infinite wifdom of the Creator, as in objects of
the greateft magnitude. It appears to me, that the
eonfideration of thefe minute fpecies, each of which
is followed by another inconceivably: more minute,
ought to make the livelieft impreflion on our minds,
and infpire us with the moil fublime ideas of the
works of the Almighty, whofe power knows no
bounds, whether as to great objects or fmall.
To imagine that after having divided a body into
a great number of parts, we arrive, at length, at
particles fo fmall as to defy all farther divifion, is
therefore the indication of a very contracted mind.
But fuppofing it poffible to defcend to particles fo
minute
42 REFLECTIONS ON DIVISIBILITY, &C.
minute as to be, in their own nature; no longer di-
vifible, as in the cafe of the fuppofed monads ; be-
fore coming to this point, we fhall have a particle
compofed of only two monads, and this particle
will be of a certain magnitude or extenfion, other-,
wife it could not have been divifible into thefe two
monads. Let us farther fuppofe, that this particle,
as it has fome extenfion, may be the thoufandth part
of an inch, or ftill fmaller if you will ; for it is of no
importance, what I fay of the thoufandth part of an
inch may be faid with equal truth of every fmaller
part. This thoufandth part of an inch, then, is com*
pofed of two monads, and confequently two monads
together would be the thoufandth part of an inch,
and two thoufand times nothing, a whole inch ; the
abfurdity ftrikes at firft fight.
The partifans of the fyftem of monads accordingly
ftnink from the force of this argument, and are re-
duced to a terrible nonplus when afked how many
monads are requifite to conftitute an extenfion. Two,
they apprehend, would appear infufEcient, they there-
fore allow that more muft be neceftary. But, if two
monads cannot ^conftitute extenfion, as each of the
two has none j neither three, nor four, nor any
number whatever will produce it ; and this com-
pletely fubverts the fyftem of monads.
yb May, 176 1. ♦
LETTER
REPLY TO THE OBJECTIONS, fee, 43
LETTER XII,
Reply to the QbjccTwns of the Monadifts to Divifibiiity
in infinitum.
T
HE partifans of monads are far from fubmitting
to the arguments adduced to eftablifh the di-
vifibility of body to infinity. Without attacking
them directly, they allege that divifibiiity in infinitum
is a chimera of geometricians, and that it is involved
in contradiction. For, if each body is divifible to
infinity, it would contain an infinite number of parts,
the fmalleft bodies as well as the greateft : the number
of thefe particles to which divifibiiity in infinitum
would lead, that is to fay, the moft minute of which
bodies are compofed, will then be as great in the
fmalleft body as in the largeft, this number being in-
finite in both ; and hence the partifans of monads
triumph in their reafoning as invincible. For, if the
number of ultimate particles of which two bodies
are compofed is the fame in both, it muft follow, fay
they, that the bodies are perfectly equal to each other.
Now this goes on the fuppofition, that the ulti-
mate particles are all perfectly equal to each other ;
for if fome were greater than others, it would not be
furprizing that one of the two bodies fhould be much
greater than the other. But it is abfolutely neceffary,
lay they, that the ultimate particles of all bodies
mould be equal to each other, as they no longer have
any extenfion, and their magnitude abfolutely va.
nifties^
44 RFPLY TO THE OBJECTIONS
nifhes, or becomes nothing. They even form a new
objection, by alleging that all bodies would be com-
pofed of an infinite number of nothings, which is a
ftill greater abfurdity,
I readily admit this ; but I remark at the fame
time, that it ill becomes them to raife fuch an ob-
jection, feeing they maintain, that all bodies are
compofed of a certain number of monads, though,
relatively to magnitude, they are abfolute nothings :
fo that by their own confeilion, feveral nothings are
capable of producing a body. They are right in
faying their monads are not nothings, but beings en-
dowed with an excellent quality, on which the na-
ture of the bodies which they compofe is founded.
Now, the only queftion here is refpecling exteniion ;
and as they arc under the neceffity of admitting that
their monads have none, feveral nothings, according
to them, would always be fomething.
■ But I mall pufh this argument againft the fyftem
of monads no farther ; my object being to make a
direct reply to the objection founded on the ultimate
particles of bodies, raifed by the monadifts in'fupport
of their fyftem, by which they flatter themfelves in
the confidence of a complete victory over the parti-
fans of divisibility in infinitum.
I fhould be glad to know, in the firft place, what
they mean by the ultimate particles of bodies. In
their fyftem, according to which every body is com-
pofed of a certain number of monads, I clearly com-
prehend that the ultimate particles of a body, are the
monads themfelves which conftitute it j but in the
fyftem
OF THE MONADISTS. 45
fyftem of divisibility in infinitum, the term ultimate
particle is abfolutely unintelligible.
They are right in faying, that thefe are the par*
tides at which we arrive from the divifion of bodies,
after having continued it to infinity. But this is
juft the fame thing with faying, after having finifncd
a divifion which never comes to an end. For divi-
fibility in infinitum means nothing elfe but the pof-
fibility of always carrying on the divifion, without
ever arriving at the point where it would be neceffary
to ftop. He who maintains divifibility in infinitum,
boldly denies, therefore, the exiftence of the ultimate
particles of body ; and it is a manifeft contradiction,
*o fuppofe at once ultimate particles and divifibility
in infinitum.
I reply, then, to the partifans of the fyftem of
monads, that their objection to the divifibility of
body to infinity would be a very folid one, did that
fyftem admit of ultimate particles; but being ex-
prefsly excluded from it, all this reafoning, of courfe,
falls to the ground.
It is falfe, therefore, that in the fyftem of divifibi-
lity in infinitum, bodies are compofed of an infinity
of particles. However clofely connected thefe two
propofitions may appear to the partifans of monads,
they manifestly contradict each other ; for whoever
maintains that body is divifible in infinitum, or with-
out end, abfolutely denies the exiftence of ultimate
particles, and confequently has no concern in the
queftion. The term can only mean fuch particles as
are no longer divifible, an idea totally inconfiftent
with
46 STRONGEST SUPPORT
with the iyfbm of diviiibility in infinitum. This
formidable attack, then, is completely repelled.
1 2 lb Iday, 1 761.
LETTER .XIII.
Principle of the fatisfying Reafon, the firongefi Support
of the Monadijis.
"OU muft be perfectly fenftble that one of the
two fyftem s, which have undergone fuch ample
difcufiion, is necelfarily true, and the other falfe, fee-
ing they are contradictory.
It is admitted on both fides, that bodies are divi-
sible : the only queflion is, Whether this diviiibility
is limited ? or Whether it may always be carried
farther, without the poftibility of ever arriving at
indivifible particles ?
The fyftem of monads is eftablifhed in the former
cafe, fince after having divided a body into indivifible
particles, thefe very particles are monads, and there
would be reafon for faying that all bodies are com-
pofed of them, and each of a certain determinate
number. Whoever denies the fyftem of monads,
muft likewife, then, deny that the diviiibility of bo-
dies is limited. He is under the neceflity of main-
taining, that it is always poiiible to carry this diviii-
bility farther, without ever being obliged to ftop;
and this is the cafe of diviiibility in infinitum, on
which fyftem we abfolutely deny the exiftence of ul-
timate particles : confequently the difficulties refult-
ing
OF THE MONADISTS. 47
ing from their infinite number fall to the ground of
themfelves. In denying monads, it is impoffible to
talk any longer of ultimate particles^ and Hill lefs of
the number of them which enters into the compo-
fition of each body. ,
You muft have remarked, that what I have hitherto
produced in fupport of the fyftem of monads is defti-
tute of folidity. I now proceed to inform you that
its fupporters reft their caufe chiefly on the great
principle of the fufficient reafon, which they know
how to employ fo dexteroufly, that by means of it
they are in a condition to demonftrate whatever
fuits their purpofe, and to demolifh whatever makes
againft them. The blelTed diicovery made, then, is
this, That nothing can be without a fufficient reafon;
and to modern phiiofophers we Hand indebted for it.
In order to give you an idea of this principle, you
have only to confider, that in every thing prefented
to you, it may always be alked, Why it is fuch ? And
the anfwer is what they call the fufficie?it reafon, fup-
pofing it really to correfpond with the queftion pro-
pofed. Wherever the why can take place, the pof-
fibility of a fatisfactory anfwer is taken for granted,
which {hall, of courfe, contain the fufEcient reafon of
the thing.
This is very far, however, from being a myftery
of modern difcovery. Men in every age have alked
why ; an inconteftable proof of their conviction that
every thing muft have a fatisfying reafon of its exift-
ence. This principle, that nothing is without a caufe,
was very well known to ancient phiiofophers ; but
unhappily
48 STRONGEST SUPPORT
unhappily tliis caufe is for the mod part concealed
from us. To little purpofe do we afk why : no one
is qualified to affign the reafon. It is not a matter of
doubt j that every thing has its caufe ; but a progrefs
thus far hardly deferves the name ; and fo long as it
remains concealed, we have not advanced a {ingle
Hep in real knowledge.
You may perhaps imagine, that modern philofo-
phers, who make fuch a boaft of the principle of a
fatisfying reafon, have actually difcovered that of all
things, and are in a condition to anfwer every why
that can be propofed to them; which would un-
doubtedly be the very fummit of human knowledge;
but, in this refpect, they are juft as ignorant as their
neighbours : their whole merit amounts to no more
than a pretenfion to have demonflrated, that where-
ever it is poffible to afk the queftion why, there muft
be a fatisfying anfwer to it, though concealed from us.
They readily admit, that the ancients had a know-
ledge of this principle, but a knowledge very obfcure ;
whereas they pretend to have placed it in its cleareft
light, and to have demonftrated the truth of it : and
therefore it is that they know how to turn it moft to
their account, and that this principle puts them in a
condition to prove, that bodies are compofed of
monads.
Bodies, fay they, muft have their fufEcient reafon
fomewhere ; but if they were divifible to infinity,
fuch reafon could not take place : and hence they
conclude, with an air altogether philofophic, that, as
every thing mujl have its fujjicient reafon, it is abfolutely
6 necejfary
OF THE MONADISTS. 49
rteceffary that all bodies Jhould be compofed of monads:
which was to be demonftrated. This, I muft admit,
is a demonftration not to be refilled.
It were greatly to be wifhed that a reafoning fo
flight could elucidate to us queftions of this import-
ance ; but I frankly confefs, I comprehend nothing
of the matter. They talk of the fufticient reafon of
bodies, by which they mean to reply to a certain
wherefore, which remains unexplained. But it would
be proper, undoubtedly, clearly to underftand, and
carefully to examine a queftion, before a reply is at-
tempted -> in the prefent cafe, the anfwer is given
before the queftion is formed.
Is it afked, Why do bodies exift ? It would be ri-
diculous, in my opinion, to reply, Becaufe they are
compofed of monads ; as if they contained the caufe
of that exiftence. Monads have not created bodies :
and when I ail?:, Why fuch a being exifts ? I fee no
other reafon that can be given but this, Becaufe the
Creator has given it exiftence ; and as to the manner
in which creation is performed, philofophers, I think,
would do' well honeftly to acknowledge their igno-
rance.
But they maintain, that God could not have pro-
duced bodies, without having created monads, which
were neceffary to form the compofition of them.
This manifeftly fuppofes, that bodies are compofed
pf monads, the point which they meant to prove by
this reafoning. And you are abundantly fenfible,
that it is not fair reafoning to take for granted the
truth of a proportion which you are bound to prove
Vol. II. E by
$0 ANOTHER ARGUMENT
by reafoning. It is a fophifm known in logic by the
name of a petitio principii, or, begging the queftion*
ibtbMay, 1761.
LETTER XIV.
Another Argument of the Monadi/is, derived from the
Principle of the fufficient Reafon. Abfurdities re-
fusing from it,
HPHE partifans of .monads likewife derive their
grand argument from the principle of the fa-
tisfying reafon, by alleging that they could not even
comprehend the poffibility of bodies, if they were
divifible to infinity, as there would be nothing in
them capable of checking imagination : they mult
have ultimate particles or elements, the compolition
of which muft ferve to explain the compolition of
bodies.
But do they pretend to underftand the poffibility
of all the things which exift ? This would favour too
much of pride ; nothing is more common among
philofophers than this kind of reafoning : I cannot
comprehend the poffibility of this, unlefs it is fuch
as I imagine it to be : therefore it neceffarily muft be
fuch.
You clearly comprehend the frivoloufnefs of fuch
reafoning j and that in order to arrive at truth, re-
fear'ch much more profound muft be employed. Ig-
norance can never become an argument to conduct
us to the knowledge of truth, and the one in queftion
is
OF THE MONADISTS* 5 1
is evidently founded on ignorance of the different
manners which may render the thing; poflible.
But on the fuppoiition that nothing exifts but
that whofe poiTIbility they are able to comprehend,
is it poffible for them to explain how bodies would
be compofed of monads ? Monads, having no exten-
fion, mull be confidered as points in geometry, or as
we reprefent to ourfelves fpirits and fouls* Now it
is well known that many geometrical points, let the
number be fuppofed ever fo great, never can pro-
duce a line, and confequently ftill lefs a furface, or a
body. If a thoufand points were fufficient to con-
ftitute the thoufandth part of an inch, each of thefe
muft neceffarily have an extenfion, which, taken a
thoufand times, would become equal to the thou-
fandth part of an inch. Finally, it is an incontestable
truth, that take any number of points you will, they
never can produce extension. I fpeak here of points
fuch as we conceive in geometry, without any length,
breadth or thicknefs, and which in that refpecl, are
abfolutely nothing.
Our philofophers accordingly admit that no eX-
tenfion can be produced by geometrical points, and
they folemnly protefl that their monads ought not
to be confounded with thefe points. They have no
more extenfion than points, fay they ; but they are
invefted with admirable qualities > fuch as reprefent-
ing to them the whole univerfe by ideas, though ex-
tremely obfeure ; and thefe qualities render them
proper to produce the phenomenon of extenfion, or
rather that apparent extenfion which I formerly
E 2 mentioned.
£2 ANOTHER ARGUMENT
mentioned. The fame idea, then , ought to be formed
of monads as of fpirits and fouls, with this difference,
that the faculties of monads are much more imper-
feft.
The difficulty appears to me by this greatly in-
creafed, and I flatter myfelf you will be of my opi-
nion, that two or more fpirits cannot poffibly be
joined fo as to form extenfion. Several fpirits may
very well form an affernbly, or a council, but never
an extenfion ; abftraction made of the body of each
counfellor, which contributes nothing to the delibe-
ration going forward, for this is the production of
fpirits only ; a council is nothing elfe but an affernbly
of fpirits or fouls : but could fuch an affernbly re-
prefentan extenfion? Hence it follows, that monads
are flill lefs proper to produce extenfion than geo-
metrical points are.
The partifans of the fyflem, accordingly, are not
agreed as to this point. Some allege, that monads
are actual parts of bodies ; and that after having di-
vided a body as far as poffiple, you then arrive at
the monads which conftitute it.
Others abfolutely deny that monads can be con-
fidered as conftituent parts of bodies ; according to
them, they contain only the fufficient reafon : while
the body is in motion, the monads flir not, but they
contain the fufficient reafon of motion. Finally,
they cannot touch each other ; thus, when my hand
touches a body, no one monad of my hand touches
a monad of the body.
What is it then, you will afk, that touches in this
cafe,,
OF THE MONADISTS. $$
cafe, if it is not the monads which compofe the hand
and the body ? The anfwer muil be, that two no-
things touch each other, or rather it muft be denied
that there is a real contact. It is a mere iilufion defti-
tute of all foundation. They are under the neceifity
of affirming the fame thing of all bodies, which ac-
cording to thefe philofophers are only phantoms
formed by the imagination, reprefenting to itfelf
very confufedly the monads which contain the fuf-
ficient reafon.of all that we denominate body.
In this philofophy every thing is fpirit, phantom
and iilufion ; and when we cannot comprehend thefe
myfteries, it is our ftupidity that keeps up an attach-
ment to the grofs notions of the vulgar.
The greateft fingularity in the cafe is, that thefe
philofophers, with a defign to inveftigate and explain
the nature of bodies and of exteniion, are at laft re-
duced to deny their exiftence. This is undoubtedly
the fureft way to fucceed in explaining the pheno-
mena of nature ; you have only to deny them, and
to allege, in proof, the principle of the fuffieient
reafon. Into fuch extravagancies will philofophers
run, rather than acknowledge their ignorance.
19/16 Mny, I 761.
LETTER XV.
Refctlions on the Svjiem of Monads.
rT would be a great pity, however, that this inge-
A nious fyftem of monads fhould crumble into ruins.
It has made too much noife, it has coft its partifans
E 3 too
54 REFLECTIONS ON THE
too many fublime and profound fpeculations, to be
permitted to fink into total oblivion. It will ever
remain a finking monument of the extravagance
into which the fpirit of philofophizing may run. It
is well worth while, then, to prefent you with a
more particular account of it.
It is necefiary, firft of all, to banifli from the mind
every thing corporeal, all extenfion, all motion, all
time and fpace, for all thefe are mere illufion. No-
thing exifls in the world but monads, the number of
which undoubtedly is prodigious. No one monad
is to be found in connection with others ; and it is
demonstrated by the principle of the fuflicient rea-
fon, that monads can in no manner whatever act
upon each other. They are indeed invefted with
powers, but thefe exerted only within themfelves,
without having the leaft influence externally.
Thefe powers, with which each monad is endowed,
have a tendency only to be continually changing
their own ftate, and confift in the reprefentation of
all other monads. My foul, for example, ■ is a mo-
nad, and contains in itfelf ideas of the ftate of all
other monads. Thefe ideas are for the moft part
very obfcure; but the powers of my foul are conti-
nually employed in their farther elucidation, and in
carrying them to a higher degree of clearnefs.
Other monads have, in this refpect, a fuflicient re-
femblance to my foul ; each is replete with a prodi-
gious quantity of obfcure ideas of all other monads,
and of their ftate j and they are continually exert-
ing themfelves with more or lefs fuccefs in unfolding
thefe
SYSTEM OF MONADS. $$
thefe ideas, and in carrying them to a higher degree
of clearnefs.
Such monads as have fucceeded better than I have
done are fpirits more perfect ; but the greater part
flili remain in a ftate of ftagnation, in the greateft
obfeurity of their ideas; and when they are the ob-
ject of the ideas of my foul, they produce in it the
illufory and chimerical idea' of extenfion, and of
body. As often as my foul thinks of bodies and of
motion, this proves that a great quantity of other
monads are ftill buried in their obfeurity; it is like-
wife when I think of them, that my foul forms with-
in itfelf the idea of fome extenfion, which is confe-
quently nothing but mere illufion.
The more monads there are plunged in the abyfs
of the obfeurity of their ideas, the more is my foul
dazzled with the idea of extenfion ; but when they
come to clear up their obfeure ideas, exteniion feems
to me to diminifh, and this produces in my foul the
illufory idea of motion.
You will afk, no doubt, How my foul perceives
that other monads fucceed in developing their ob-
feure ideas, feeing there is no connection between
them and me? The partifans of the fyftem of mo-
nads are^ ready with this reply, that it takes place
conformably to the perfect harmony which the Cre-
ator (who is himfelf only a monad,) has eftabliilied
between monads, by which each perceives in itfelf,
as in a mirror, every developement produced in
'others, without any manner of connection between
them.
E 4 It
$6 REFLECTIONS ON THE
It is to be hoped, then, that all monads may at
length become fo happy as to clear up their obfcure
ideas, and then we mould lofe all ideas of body and
of motion; and the illufion, arifmg- merely from the
obfcurity of ideas, would entirely ceafe.
But there is little appearance of the arrival of this
bleffed ftate; moll monads, after having acquired
the capacity of clearing up their obfcure ideas, fud-
denly relapfe. When fhut up in my chamber, I per-
ceive myfelf but of fin all extenfion, becaufe feveral
monads have then unfolded their ideas: but as fpon
as I walk abroad, and contemplate the vaft expanfe
of heaven, they niuft all have relapfed into their
ftate of dulnefs.
There is no change of place or of motion; all
that is illufion merely : my foul remains almoft al-
ways in the fame place, juft as all other monads.
But, when it begins to unfold fome ideas, which be<
fore were but very obfcure, it appears to me then
that I am approaching the object which they repre-
fent to me, or rather that which the monads of fuch
idea excite in me : and this is the real explanation
of the phenomenon, when it appears to us that we
are approaching to certain objects.
It happens but too frequently that the elucidations
we had acquired are again loft ; then it appears to
us that we are removing from, the fame object. And
here we muft look for the true folution of our jour-
neyings. My idea, for example, of the city of Mag-
deburg is produced by certain monads, of which at
prefent I have but very obfcure ideas ; and this is
the
SYSTEM OF MONADS. 57
the reafon why I confider myfelf as at a diftance from
Magdeburg. Laft year, thefe fame ideas fuddenly
became clear, and then I imagined I was travelling
to Magdeburg, and that I remained there feveral
days. This journey, however, was an illufion merely,
for my foul never ftirs from its place. It is likewife
an illufion when you imagine yourfelf abfent from
Berlin, becaufe the confufed representation of certain
monads excites an obfcure idea of Berlin, which you
have only to clear up, and that inftant you are at
Berlin. Nothing more is neceffary. What we call
journeys, and on which we expend fo much money,
is mere illulion. Such is the real plan of the fyitem
of monads.
You will aik, Is it poffible there ever fhould have
been perfons of good fenfe, who ferioufly maintained
thefe extravagances ? I reply, there have been but
too many, that I know feveral of them, that there
are fome at Berlin, nay perhaps at Magdeburg.
23d Miy, 1761.
LETTER XVI.
Continuation,
HPHE fyftem of monads, fuch as I have been de-
fcribing it, is a neceffary confequence from the
principle, that bodies are compounded of iimple be-
ings. The moment this principle is admitted, you
are obliged to acknowledge the juftnefs of all the
other confequences, which refult from it fo naturally,
that
5 & REFLECTIONS ON THE
that it is impoffibie to reject, any one, however ab-
fm'd and contradictory.
Firft, thefe fimple beings, which mull enter into
the compofition of bodies, being monads which have
no exteniion, neither can their compounds, that is
bodies, have any; and all thefe exteniion s become
iliufion, chimera, it being certain, that parts defd-
tute of exteniion are incapable of producing a real
exteniion ; it can be, at moll, an appearance, or a
phantom which dazzles by a fallacious idea of ex-
teniion. In a word, every thing becomes illulion,
and upon this is founded the fyftem of pre-eitablilhed
harmony, the difficulties of which I have already
pointed out.
It is neceffary then to take care that we be not en-
tangled in this labyrinth of abfurdities. If you make
a fingle falfe Hep over the threlhold, you are in-
volved beyond the power of efcaping. Every thing
depends on the firil ideas formed of exteniion ; and
the manner in which the partifans of the fyltern of
monads endeavour to eftablilh it, is extremely re-
ductive.
Thefe philofophers love not to fpeak of the ex-
teniion of bodies, becaufe they clearly forefee, that
it lTmft become fatal to them in the fequel j but in-
ftead of faying, that bodies are extended, they de-
nominate them compound beings, /which no one can
deny, as exteniion neceffarily fuppofes divisibility,
and confequently a combination of parts which con-
ftitute bodies. But they prefently make a wrong
ufe of this notion of a compound being, for, fay
they,
SYSTEM OF MONADS. 59
tliey, a being can be compounded only fo far as it is
made up of fimple beings ; and hence they conclude,
that every body is compounded of fimple beings.
As foon as you grant them this conclufion, you are
caught, beyond the power of retreating; for you are
under the neceffity of admitting, that thefe fimple
beings, not being compounded, are not extended.
This captious argument is exceedingly feductive.
If you permit yourfelf to be dazzled with it, they
have gained their point. Only admit this propofl-
tion, bodies are compounded of fimple beings, that
is, of parts which have no extenfion, and you are •
entangled. With all your might, then, refift this
affertion : every compound being is made up of fimple
beings ; and though you may not be able directly to
prove the fallacy, the abmrd confequences which
immediately remit, would be fufEcient to over-
throw it.
In effect, they admit that bodies are extended ;
from this point the partifans of the fyftem of mo-
nads fet out, to eftablifh the proportion that they
are compound beings; and having hence deduced,
that bodies are compounded of fimple beings, they
are obliged to allow, that fimple beings are incapable
of producing real extenfion, and confequently, that
the extenfion of bodies is mere illufion.
An argument whofe conclufion is a direct contra-
diction of the premifes is Angularly jxrange : this
reafoninsj fets out with advancing that bodies are ex-
tended; for, if they were not, how could it be
known that they are compound beings, and then
comes
6o REFLECTIONS ON THE
comes the conclusion, that they are not fo. Never
was a fallacious argument, in my opinion, more com-
pletely refuted than this has been. The queftion
was, Why are bodies extended? And, after a little
turning and winding, it is anfwered, Becaufe they
are notfo. Were I to be afked, Why has a triangle
three fides ? and I mould reply, that it is a mere S-
lufion, would fuch a reply be deemed fatisfaciory ?
It is therefore certain, that this proportion, ' Every
compound being is neceffarily made up of fimple be-
ings,' leads to a falfe conclufion, however well-founded
it may appear to the partifans of monads, who even
pretend to rank it among the axioms, or firft prin-
ciples of human knowledge. The abfurdity in which
it immediately iffues, is fuflicient to overturn it, were
there no other reafons for calling it in queftion.
But as a compound being here means the fame
thing as an extended being, it is juft as if it were
affirmed, ' Every extended being is compounded of
beings which are not fo.' And this is precifely the
queftion. It is afked, Whether, on dividing a body,
you arrive at length at parts uniufceptible of any
farther divifion, for want of extenfion ; or, Whether
you never arrive at particles fuch as that the divifi-
bility mould be unbounded ?
In order to determine this important queftion,
for the fake of argument let it be fuppofed, that
every body is compounded of parts without exten-
fion. Certain fpecious reafonings may eafilybe em-
ployed, drawn from the noted principle of the fuf-
ficient rcafon; and it will be faid, that a compound
2 beings
SYSTEM OF MONADS. 6 1
being can have its fufficient reafon only in the fimple
beings which compofe it ; which might be true, if
the Compound being were in fact made up of fimple
beings, the very point in queftion; and whenever
this composition is denied, the fufficient reafon be-
comes totally inapplicable.
But it is dangerous to enter the lifts with perfons
who believe in monads ; for, befides that there is
nothing to be gained, they loudly exclaim that you
are attacking the principle of the fufficient reafon,
which is the bafis of all certainty, even of the exig-
ence of God. According to them, whoever refufes
to admit monads, and rejects the magnificent fabric,
in which every thing is illufion, is an infidel and an
atheift. Sure I am that fuch a frivolous imputation
will not make the flighted: impreffion on your mind,
but that you will perceive the wild extravagancies
into which men are driven, when they embrace the
fyftem of monads, a fyftem too abfurd to need a
refutation in detail ; their foundation being abfo-
lutely reduced to a wretched abufe of the principle
of the fufficient reafon.
ibth May, 1 76 1.
>»•?:-«<
LETTER XVII.
Conclufion of Reflections on this Syflem.
TX7"E are under the neceffity of acknowledging
the divifibility of bodies in infinitum, or of
admitting the fyftem of monads with all the extrava-
gancies
62 REFLECTIONS ON THE
gancies refulting from it ; there is no other choice !
an alternative which fupplies the partifans of that
fyftem with another formidable argument in fupport
of it.
They pretend that, by divifibility in infinitum, we
are obliged to afcribe to bodies an infinite quality,
whereas it is certain that God alone is infinite.
The partifans of the fyftem of monads are very
dangerous perfons ; they accufed us of atheifm, and
now they charge us with polytheifm, alleging that
we afcribe to all bodies infinite perfections. Thus
we mould be much worfe than pagans, who only
worfhip certain idols, whereas we are accufed of pay-
ing homage to all bodies as fo many divinities. A .
dreadful imputation, no doubt, were it well founded;
and I mould certainly prefer embracing the fyftem
of monads, with all the chimeras and illufions which
flow from it, to a declaration in favour of divifibility
in infinitum, if it involved a conclufion fo impious.
You will allow that to reproach one's adverfaries
with atheifm or idolatry is a very ftrange mode of
arguing j but where do they find us afcribing to bo-
dies this divine infinity ? Are they infinitely power-
ful, wife, good, or happy ? By no means : we only
affirm, that on dividing bodies, though the divifion
be carried on ever fo far, it will always be pofiible
to continue it farther, and that you never can arrive
I at indivifible particles. It may accordingly be af-
i firmed that the divifibility of bodies is without limits ;
and it is improper to ufe the term infinity which is
f applicable to God alone.
I muft.
SYSTEM OF MONADS; - 63
I muft remark at the fame time, that the word
1 infinity' is not fo dangerous as thefe philofophers
infinuate. In faying, for example, infinitely wicked,
nothing is more remote from the perfections of God.
They admit that our fouls will never have an end,
and thus acknowledge an infinity in the duration of
the foul, without marking the leaft difrefpect to the
infinite perfections of God. Again, when you afk
them if the extent of the univerfe is bounded, are
they very indecilive in their anfwer ? Some of them
frankly allow, that the extent of the univerfe may
very probably be infinite, without our being able,
however far our ideas are carried, ^tq. determine its
limits. Here then is one infinity more, which they
do not deem heretical.
For a ftill ftronger reafon divifibility in infinitum
oii9'ht not to give them the leaft offence. To be di-
vifible to infinity is not furcly an attribute which any
one could ever think of afcribing to the Supreme
Being, and confers not on bodies a degree of perfec-
tion which would not be far from that which thefe
philofophers allow them, in compounding them of
monads, which, on their fyftem, are beings endowed
with qualities fo eminent, that they hefitate not to
give to God himfelf the denomination of monad.
In truth, the idea of a divifion which may be con-
tinued without any bounds, contains fo little of the
character of the Deity, that it rather places bodies in
a rank far inferior to that which fpirits and our fouls
occupy ; for it may well be affirmed, that a foul, in
its effence, is infinitely more valuable than all the
bodies
64 REFLECTIONS ON THE
bodies in the world. But, on the fyftem of monads,
every body, even the vileft, is compounded of a vaft
number of monads, whofe nature has a great refem-
blance to that of our fouls. Each monad reprefents
to itfelf the whole world as eafily as our fouls j but,
fay they, their ideas of it are very obfcure, though
we have already clear, and fometimes alfo diftinci,
ideas of it. ♦.
But what affurance have they of this difference ?
Is it not to be apprehended that the monads which
compofe the pen wherewith I am writing, may have
ideas of the univerfe much clearer than thofe of my
foul ? How can I be affured of the contrary ? I ought
to be aihamed to employ a pen in conveying my
feeble conceptions, while the monads of which it
conlifts poffibly conceive much more fublimely ; and
you might have greater reafon to be fatisfied, fliould
the pen commit its own thoughts to paper, inftead of
mine.
In the fyftem of monads, that is not neceffary ; the
foul reprefents to itfelf, beforehand, by its inherent-
powers, all the ideas of my pen, but in a very obfcure
manner. What I am now taking the liberty to fug-
geft, contributes abfolutely nothing to your informa-
tion. The partifans of this fyftem have demonftrated
that fimple beings cannot exercife the flighteft influ-
ence on each other ; and your own foul derives from
itfelf what I have been endeavouring to convey, with-
out my having any concern in the matter.
Converfation," reading and writing, therefore, are
merely chimerical and deceptive formalities, which
illufion
NATURE OF COLOURS. 65
illufion would impofe upon us as the means of ac-
quiring and extending knowledge. But I have al-
ready had the honour of pointing out to you the
wonderful confequences refulting from the fyftem of
the pre-eftablifhed harmony ; and I am apprehenfive
that thefe reveries may have become too fevere a
trial of your patience, though many perfons of fupe-
rior illumination confider this fyftem as the moft
fublime production of human underftanding, and are
incapable of mentioning it but with the moft pro-
found refpect.
I flatter myfelf that I have guarded you fufEciently
againfl fuch chimeras, however feductive their ap-
pearance -> I mould be forry, at the fame time, to have
injured in your good opinion a conliderable part of
our modern philofophers. They are, for the mofl
part, extremely innocent, but remain obftinately at-
tached to the fyftem which at firft impofed on them,
without greatly troubling themfelves about the ab-
furd confequences which flow from it.
$Qtb May, ij6l.
LETTER XVIII.
Elucidation refpecling the Nature of Colours.
[" AM under the neeeility of acknowledging, that
-*- the ideas refpecling colour, which I have already
taken the liberty to fuggeft,* come far fhort of that
* Vol. I. Letters XXVII. XXVIII. and XXXI.
Vol. II, F degree
66 ELUCIDATION RESPECTING
degree of evidence to which I could have wifhed to
carry them. This fubject has hitherto proved a
ftumbling-block to philofophers, and I muft not flat-
ter myfelf with the belief that I am able to clear it of
every difficulty. I hope, at the fame time, that the
elucidations which I am going to fubmit to your ex-
amination, may go far toward removing a confider-
able part of them'.
The ancient philofophers ranked colours among
the bodies of which we know only the names. When
they were alked, for example, why fuch a body was
red, they anfwered, it was in virtue of a quality
which made it appear red. You muft be fenfible
that fuch an anfwer conveys no information, and
that it would have been quite as much to the purpofe
to confefs ignorance.
Defcartes, who firft had the courage to plunge
into the myfteries of nature, afcribes colours to a
certain mixture of light and fhade, which laft being
nothing elfe but a want of light, as it is always found
where the light does not penetrate, muft be incapable
of producing the different colours we obferve.
Having remarked that the fenfations of the organ
of fight are produced by the rays which ftrike that
organ, it neceffarily follows, that thofe which excite
in it the fenfation of red, muft be of quite a different
nature from thofe which produce the fenfation of the
other colours ; hence it is Cafily comprehended that
each colour is attached to a certain quality of the
rays which ftrike the organ of vifton. A body ap-
pears
THE NATURE OF COLOURS. 6f
pears to us red, when the rays which it emits are of
a nature to excite in our eyes the fenfation of that
colour*
The whole, then, refults in an enquiry into the
difference of the rays which variety of colours pro-
duces. This difference muft be great, to produce fo
many particular fenfations in our eyes. But wherein
can it confift ? This is the great queftion, toward
the fblution of which our prefent refearch is directed.
The firft difference between rays which prefents
itfelf is, that fome are ftronger than others. It can-
not be doubted that thofe of the fun, or of any other
body very brilliant, or very powerfully illuminated,
muft be much ftronger than thofe of a body feebly
illuminated, or endowed with a flender degree of
light j our eyes are affuredly ftruck in a very different
manner by the one and by the other.
Hence it might be inferred, that different colours
refult from the force of the rays of light ; fo that the
moft powerful rays mould produce, for example, red ;
thofe which are lefs fo, yellow ; and in progreffion,
green, and blue.
But there is nothing more eafy than to overturn
this fyftem, as we know from experience that the
fame body always appears to be of the fame colour,
be it lefs or more illuminated, or whether its rays be
ftrong or feeble. A red body, for example, appears
equally red, expofed to the brighteft luftre of the fun,
and in the ftiade, where the rays are extremely faint.
We muft not then look for the caufe of the difference
of colour in the different degrees of the force of rays
F2 of
68 NATURE OF COLOURS.
of light, it being poffible to reprefent the fame colour
as well by very forcible as by very faint rays. The
feebleft glimmering ferves equally well to difcover to
us difference of colours, as the brighteft effulgence.
It is abfolutely neceffary, therefore, that there
mould be another difference of rays difcovered, which
may characterize their nature relatively to the dif-
ferent colours. You will undoubtedly conclude, that
in order to difcover this difference, we muft be better
acquainted with the nature of luminous rays ; in
other words, we muft know what it is that, reaching
cur eyes, renders bodies vifible : this definition of a
ray muft be the jufteft, as in effect it is nothing elfe
but that which enters into the eye by the pupil, and
excites the fenfation in it.
I have already informed you, that there are only
two fyftems or theories which pretend to explain the
origin and nature of rays of light. The one is that
of Newton, who confiders them as emanations pro-
ceeding from the fun and other luminous bodies \
and the other, that which I have endeavoured to de-
monftrate, and of which I have the reputation of
bein^ the author, though others have had nearly the
fame ideas of it. Perhaps I may have fucceeded
better than they, in carrying it to a higher degree
of evidence. It will be of importance, then, to fliew,
in both fyftems, on what principle the difference of
colours may be eftablifhed.
In that of emanation, which fuppofes the rays to
iftue from luminous bodies, in the form of rivers, or
rather of fountains, fpouting out a fluid in all direc-
. ; tions,
THE ANALOGY, &C. 69
tions, it is alleged that the particles of light differ in
fize or in fubftance, as a fountain might emit wine,
oil, and other liquids j fo that the different colours
are occafioned by the diverfity of the fubtile matter
which emanates from luminous bodies. Red would
be, accordingly, a fubtile matter iffuing from the lu-
minous body, and fo of yellow and the other colours.
This explication would exhibit clearly enough . the
origin of the different colours, if the fyftem itfelf had
a folid foundation. I fhall enter into the fubject
more at large in my next letter.
zd June, 1 761.
LETTER XIX.
Reflexions on the Analogy between Colours and Sounds,
YOU will be pleafed to recollect the objections I
offered to the fyftem of the emanation of light.*
They appear to me fo powerful, as completely to
overturn that fyftem. I have accordingly fucceeded
in my endeavours to convince certain natural philo-
fophers of diftinction, and they have embraced my
fentiments of the fubje& with expreilions of lingular
fatisfaction,
Rays of light, then, are not an emanation from
the fun and other luminous bodies, and confift not
of a fubtile matter emitted forcibly by the fun, and
transmitted to us with a rapidity which may well
* Vol. I. Letters XVII. and XVIII.
F3 fill
JO THE ANALOGY BETWEEN
fill you with aftonifhment. If the rays employed
only eight minutes in their courfe from the fun to
us, the torrent would be terrible, and the mafs of
that luminary, however vaft, muft fpeedily be ex-
hausted.
According to my fyftem, the rays of the fun, of
which we have a fenfible perception, do not proceed
immediately from that luminary ; they are only par-
ticles of ether floating around us, to which the fun
communicates nearer and nearer a motion of vibra-
tion, and confequently they do not greatly change
their place in this motion.
This propagation of light is performed in a manner
fimilar to that of found. A bell, whofe found you
hear, by no means emits the particles which enter
your ears. You have only to touch it when ftruck,
to be affured that all its parts are in a very fenfible
agitation. This agitation immediately communicates
itfelf to the more remote particles of air, fo that all
receive from it fucceflively a fimilar motion of vibra-
tion, which, reaching the ear, excite in it the fenfation
of found. The firings of a Vnufical inftrurnent put
the matter beyond all doubt ; you fee them tremble,
go and come. It is even poflible to determine by
calculation how often in a fecond each firing vibrates ;
and this agitation, being communicated to the par-
ticles of air adjacent to the organ of hearing, the ear
is ftruck by it precifely as often in a fecond. It is
the perception of this tremulous agitation which con-
ftitutes the nature of found. The greater the num-
ber
COLOURS AND SOUNDS. Jl
ber of vibrations, produced by the firing in a fecond,
the higher or ftiarper is the found. Vibrations lefs
frequent produce lower notes.
We find the circumftances, which accompany the
fenfation of hearing, in a manner perfectly analogous,
in that of fight.
The medium only, and the rapidity of the vibra-
tions differ. In found, it is the air through which
the vibrations of fonorous bodies are tranfmitted.
But with refpect to light, it is the ether, or that me-
dium incomparably more fubtile and more elaftic
than air, which is univerfally diffufed wherever the
air and groffer bodies leave interftices.
As often then as this ether is put into a ftate of
vibration, and is tranfmitted to the eye, it excites in
it the fentiment of vifion, which is,inthat cafe, nothing
but a fimilar tremulous motion, whereby the fmall
nervous fibres at the bottom of the eye are agitated.
You eafily comprehend, that the fenfation muff be
different, according as this tremulous agitation is
more or lefs frequent ; or according as the number
of vibrations performed in a fecond is greater or lefs*
Hence there muft refult a difference fimilar to that
which lakes place in founds, when the vibrations are
more or lefs frequent. This difference is clearly per*
ceptible by the ear, as the character of founds in re-
fpect of flat and fharp depends on it. You will re-
coiled that the note marked C in the harpficord per-
forms about i oo vibrations in a fecond ; note D 112;
note E 125; noteF 133; note G 150; note A 166;
note B 1 87 j and note C 200. Thus the nature o£
• F 4 founds
J1 THE ANALOGY BETWEEN
founds depends on the number of vibrations per-
formed in a fecond.
It cannot be doubted that the fenfe of feeing may
be likewife differently affected, according as the num-
ber of vibrations of the nervous fibres of the bottom
of the eye is greater or lefs. When thefe fibres vi-
brate i ooo times in a fecond, the fenfation muft be
quite different from what it would be, did they vi-
brate 1 200 or 1500 times in the fame fpace.
True it is that the organ of vifion is not in a con-
dition to reckon numbers fo great, ft ill lefs than the
ear is to reckon the vibrations which conftitute found;
but it is always in our power to diflinguifh between
the greater and the lefs.
In this difference, therefore, we muft look for the
caufe of difference of colour ; and it is certain that
each of them correfponds to a certain number of vi-
brations, by which the fibres of our eyes are ftruck in
a fecond, though we are not as yet in a condition to
determine the number correfponding to each parti-
cular colour, as we can do with refpect to founds.
Much refearch muft have been employed before it
was poflible to afcertain the numbers correfponding
to all the notes of the harpfichord, though there was
an antecedent conviction that their difference was
founded on the diverfity of thofe numbers. Our
knowledge reflecting thefe objects is neverthelefs
confiderably advanced, from our being affured that
there prevails a harmony fo delightful between the
different notes of the harpfichord and the different
colours ; and that the circumftances of the one ferve
to
COLOURS AND SOUNDS. 73
to elucidate thofe of the other. This analogy ac-
cordingly furnifhes the moft convincing proofs in
fupport of my fyftem. But I have reafons fall more
folid to adduce, which will fecure it from every at-
tack.
6th Juuet 1761.
LETTER XX.
Continuation.
NOTHING is more adapted to the communica-
tion of knowledge refpecHng the nature of
vifion, than the analogy difcoverable, almoft in every
particular, between it and the hearing. Colours are
to the eye what founds are to the ear. They differ
from each other as flat and fharp notes differ. Now
we know that flat and fharp in founds depends on
the number of vibrations whereby the organ of hear-
ing is ftruck in a given time, and that the nature of
each is determined by a certain number which marks
the vibrations performed in a fecond. From this I
conclude, that each colour is likewife reftricled to a
number of vibrations, which acl: on vifion ; with
this difference, that the vibrations which produce
found relide in grofs air, whereas thofe of light and
colours are tranfmitted through a medium incompa-
rably more fubtile and elaftic. The fame thing holds
as to the objects of both fenfes. Thofe of hearing
are all of them bodies adapted to the tranfmiflion of
found, that is fufceptible of a motion of vibration,
74 THE ANALOGY BETWEEN
or of a tremulous agitation, which, communicating
itfelf to the air, excites in the organ the fenfation
of a found corresponding to the rapidity of the vi-
brations.
Such are all mufical inftruments ; and, to confine
myfelf principally to the harpfichord, we afcribe to
each firing a certain found which it produces when
ftruck. Thus one firing is named C, another D,
and fo on. A firing is named C, when its ftruchire
and tenlion are fuch, that being ftruck, it produces
about 100 vibrations in a fecond; and if it produced
lefs or more in the fame time, it would have the
name of a different note, higher or lower.
You will pleafe to recollect, that the found of a
firing depends on three things, its length, its thick-
nefs, and the degree of tenlion ; the more it is
ftretched, the fliarper its found becomes: and as long
as it preferves the fame difpofition, it emits the fame
found ; but that changes as foon as the other under-
goes any variation.
Let us apply this to bodies which are the objects
of vifion. The minuter particles which compofe the
tiffue of their furface, may be confidered as firings
diftended, in as much as they are endowed with a
certain degree of elafticity and bulk, fo that being
ftruck they acquire a motion of vibration, of which
they will finilh a certain number in a fecond : and
on this number depends the colour which we afcribe
to fuch body. It is red, when the particles of its
furface have fuch a degree of tenlion, that being agi-
tated, they perform precifely fo many vibrations in
a fecond
COLOURS AND SOUNDS. 75
a fecond as are neceffary to excite in us the fenfation
of that colour, A degree of tenfion which would
produce vibrations more or lefs rapid, would excite
that of a different colour, and then the body would
be yellow, green, or blue, &c.
We have not as yet acquired the ability of afiign-
ing to each colour the number of vibrations which
conftitute its effence ; we do not fo much as know
which are the colours that require a greater or lefs
rapidity of vibration, or rather^ it is not yet deter-
mined what colours correfpond with high or low
notes. It is fufficient to know, that each colour is
attached to a certain number of vibrations, though
it has not hitherto been afcertained ; and that you
have only to change the teniion or elafticity of the
particles which form the furface of a body, to make
it change colour.
We fee that the mod beautiful colours in flowers
quickly change and difappear, from a failure of the
nutritive juices : and becaufe their particles lofe their
vigour or their teniion. This too is obfervable in
every other change of colour.
To place this in a clearer light, let us fuppofe that
the fenfation of red requires fuch a rapidity of vi-
bration, that 1 ooq are performed in a fecond ; that
orange require 1125, yellow 1250, green 1333, blue
1500, and violet 1666. Though thefe numbers are
only fuppofed, this affects not the object I have in
view. What I fay as to thefe numbers, will apply
in like manner to the really correfponding numbers,
if ever they are difcoveredr
A body,.
j6 HOW OPAQUE BODIES
A body, then, will be red, when' the particles of
its furface put in vibration, complete iooo in a.fe-
cond ; another body will be orange, when dlfpofed
fo as to complete 1 1 25 in a fecond, and fo on. Hence
it is -obvious that there muft be an endlefs variety of
intermediate colours, between the fix principal which
I have mentioned ; and it is likewife evident, if the
particles of a body being agitated mould perform
1400 vibrations in a fecond, it would be of an in-
termediate colour between green and blue ; green
correfponding to number 1333, and blue to 1500.
Qtb J une 3 176 1. ■ . . •
LETTER XXI.
How opaque Bodies are retidered vijible.
"OU will find no difficulty in the definition I
have beens giving of coloured bodies. The
particles of their furface are always endowed with
a certain degree of elafticity, which renders them
fufceptible of a motion of vibration, as a firing is
always fufceptible of a certain found ; and it is the
number of vibrations which thefe particles are ca-
pable of making in a fecond, which determines the
fpecies of colour.
If the particles of the furface have not elafticity
fufficient to admit of fuch agitation, the body muft
be black, this colour being nothing elfe but a de-
privation of light, and all bodies from which no rays
are tranfmitted to our eyes appearing black.
I now
ARE RENDERED VISIBLE. 77
I now come to a very important queftion, refpecr.-
ing which fome doubts may be entertained. It may
be afked, What is the caufe of the motion of vibra-
tion which conftitutes the colours of bodies ?
Into the difcovery of this indeed the whole is re-
folved ; for as foon as the particles of bodies mail
be put in motion, the ether diffufed through the air
will immediately receive a fimilar agitation, which,
continued to our eyes, conftitutes there that which
we call rays , from which vilion proceeds.
I remark, firft, that the particles of bodies are
not put in motion by an internal, but an external
power, juft as a ftring diftended would remain for
ever at reft, were it not put in motion by fome ex-
ternal force. Such is the cafe of all bodies in the
dark ; for, as we fee them not, it is a certain proof
that they emit no fays, and that their particles are
at reft. In other words, during the night, bodies
are in the fame ftate with the firings of an inftru-
ment that is not touched, and which emit no found ;
whereas bodies rendered vifible may be compared to
firings which emit found.
And as bodies become vifible as foon as they are
illuminated, that is as foon as the rays of the fun, or
of fome other luminous body, fall upon them, it
muft follow, that the fame caufe which illuminates
them, muft excite their particles to generate rays,
and to produce in our eyes the fenfation of viiion.
The rays of light, then, falling upon a body, put its
particles into a ftate of vibration.
This appears at firft furprizing, becaufe on ex-
pofing
7§ OPAQUE BODIES, &C
poling our hands to the ftrongeft light, no ienlible
impreffion is made on them. It is to be confidered,
that the fenfe of touch is in us too grofs to perceive
thefe fubtile and flight impreihons, but that the fenfe
of light, incomparably more delicate, is powerfully
affected by them; this furnifhes an inconteftable
proof that the rays of light which fall upon a body
poifefs fuflicient force to act upon the minuter par-
. tides, and to communicate to them a tremulous agi-
tation. And in this precifely confifts the action ne-
cefiary to explain how bodies, when illuminated, are
put in a condition themfelves to produce rays, by
means of which they become vifible to us. It is fuf-
ficient that bodies Ihould be luminous or expofed to
the light, in order to the agitation of their particles,
and thereby to -their producing themfelves rays which
render them vifible to us.
The perfect analogy between hearing and light,
gives to this explanation the highelt degree of pro-
bability. Let a harpfichord be expofed to a great
noife, and you will fee that not only the llrings in
general are put into a ftate of vibration, but you will
hear the found of each, almoft as if it were actually
touched. The mechanifm of this phenomenon is
eafily comprehended, as foon as it is known that a
firing agitated is capable of communicating to the
air the fame motion of vibration which, tranfmitted
to the ear, excites in it the fenfation of the found
which that fame ftring emits.
Now as a ftring produces in the air fuch a motion,
it follows, that the air reciprocally acts on the ftring,
and
WONDERS OF THE HUMAN VOICE. 79
and gives it a tremulous motion. And as a noife is
o
capable of putting in motion the firings of a harp-
fichord,and of extracting founds from them,the fame
thing muft take place in the objects of vifion.
Coloured bodies are fimilar to the firings of a
harpfichord, and the different colours to the different
notes, in refpect of high and low. The light which
falls on thefe bodies, being analogous to the noife to
which the harpfichord is expofed, acts on the particles
of their furface, as that noife ads on the firings of
the harpfichord, and thefe particles thus put in vibra-
tion, will produce the rays which (hall render the
body vifible.
This elucidation feems to me fufHcient to diflipate
every doubt relating to my theory of colours. I
flatter myfelf at leaft, that I have eftablifhed the true
principle of all colours, as well as explained how they
become vifible to us only by the light whereby bodies
are illuminated, unlets fuch doubts turn upon fome
other point which I have not touched upon.
\%tb Juxe, 1 76 1.
LETTER XXII.
The Wonders of the Human Voice.
TN explaining the theory of founds, I confidered
•*■ only two refpecls in which founds could differ ;
the one regarded the force of found, and I remarked
that it is greater in proportion as the vibrations ex-
cited in the air are more violent. Thus the noife of
8 a difcharge
80 WONDEkS OF THE HUMAN VOICE;
a difcharge of cannon, or the ringing of a bell, has
more force than that of a ftring, or of the human
voice.
The other difference of founds is totally indepen-
dent of this, and refers to flat and fharp, according
to which we fay fome are low and others high. My
remark relatively to this difference, made it to de-
pend on the number of vibrations completed in a
certain given time, fay a fecond ; fo that the greater
fuch number is, the higher or {harper is the found,
and the fmaller it is, the found is lower or flatter.
< You can eaiily comprehend how the fame note
may be either ftrong or faint ; accordingly we fee
that the forte and piano employed by muficians,
change in no refpect the nature of founds. Among
the good qualities of a harpfichord, it is required that
all the notes fhould have nearly the fame degree of
ftrength, and it is always conlidered as a great fault
when fome of the firings are wound up to a greater
degree of force than the reft. Now the flat and the
fliarp are referable only to the Ample founds, whofe
vibrations follow regularly, and at equal intervals ;
and, in mufic, we employ only thofe founds which
are denominated Ample. Accords are compound
founds, or the concourfe of feveral produced at once,
among the vibrations of which a certain order muft
predominate, which is the foundation of harmony.
But when no relation among the vibrations is per-
ceptible, it is a confufed noife, with which it is im-
poflible to fay what note of the harplichord is in tune,
fuch as the report of a cannon or muiket.
There
WONDERS OF THE HUMAN VOICE. 8 J
There is ftill another remarkable difference among
the fimple founds, which feems to have efcaped the
attention of philofophers. Two founds may be of
equal force, and in accord with the fame note of
the harpfi chord, and yet very different to the ear.
The found of a flute is totally different from that of
the French-horn, though both may be in tune with
the fame note of the harpiichord, and equally ftrong ;
each found derives a certain peculiarity from the in-
ftrument which emits it, but it is impoflible to de-
fcribe wherein this confifts; the fame iliing too emits
different founds according as it is ftruck, touched or
pinched. You can eafily diftinguifh the found of
the horn, the flute, and other muficalinftruments.
The moil wonderful diverfity, to fay nothing of
the variety of articulation in fpeech, is obfervable in
the human voice, that aftonilhing mailer-piece of
the Creator. Reflect but for a moment on the dif-
ferent vowels which the mouth limply pronounces
or lings. When the vowel a is pronounced or fung,
the found is quite different from that of e, /, o, u, or
ai pronounced or fung, though on the fame tone.
We mull not, then, look for the reafon of this dif-
ference in the rapidity or order of the vibrations j
no inveiligation of philofophers has hitherto un-
folded this myilery.
You mull be perfectly fen Able, that in order to
utter thefe different vowels, a different conformation
mull be given to the cavity of the mouth, and that
in man the organization of this part is much better
adapted to produce thefe effects, than that of ani-
Vql. II. G mals.
$2 WONDERS OF THE HUMAN VOICE.
mals. We find accordingly, that certain birds which
learn to imitate the human voice, are never capable
of diftinctly pronouncing the different vowels j the
imitation is, at beft, extremely imperfect..
In many organs there is a flop which bears the
name of the human voice ; it ufually, however, con-
tains only the notes which exprefs the vocal founds
ai or ae. I have no doubt, that with fome change
it might be poffible to produce likewife the other
vocal founds a9 e, i, o, u9 ou ; but even this would
not be fufficient to imitate a fingle word of the hu-
man voice; how combine them with the confonants,
which are fo many modifications of the vowels ? We
are fo conformed, that, however common the prac-
tice, it is alrnoft impoflible to trace and explain the
real mechanifm.
We diftinctly obferve three organs employed in
exprefling the confonants, the lips, the tongue, and
the palate ; but the nofe likewife effentially concurs.
On flopping it, we become incapable of pronouncing
the letters ffi and n ; the found of b and d only is
then to be heard. A firiking proof of the marvel-
lous ftru<5ture of our mouth for the pronunciation
of the letters undoubtedly is, that all the fkill of man
has not hitherto been capable of producing a piece
of mechanifm that could imitate it. The fong has
been exactly imitated, but without any articulation
of founds, and without diftinction of the different
Vowels*
The conilruction of a machine capable of exprefling
founds, with all the articulations, would no doubt be
a very
PHENOMENA OF ELECTRICITY. 83
a very important difcovery. Were it polTible to exe-
cute fuch a piece of mechanifm, and bring it to fuch
perfection, that it could pronounce all words, by
means of certain flops, like thofe of an organ or
harpfichord, every one would be furprized, and juflly,
to hear a machine pronounce whole difcourfes or
fermons together, with the mod graceful accompa-
niments. Preachers and other orators, whofe voice
is either too weak or difagreeable, might play their
fermons or orations on fuch a machine, as organifis
do pieces of mufic. The thing does not feem to me
impoflible.
i6tb June, 1 76 1.
LETTER XXIII.
A Summary of the principal Phenomena of Eleclricity,
THE fubject which I am now going to recom-
mend to your attention almoft terrifies me.
The variety it prefents is immenfe, and the enume-
ration of facts ferves rather to confound than to in-
form. The fubjecl I mean is Electricity, which, for
fome time paft, has become an object of fuch im-
portance in phyfics, that every one is fuppofed to be
acquainted with its effects.
You muft undoubtedly have frequently heard it
mentioned m converfation ; but I know not whe-
ther you have ever witneffed any of the experiments.
Natural philofophers of modern times profecute the
ftudy of it with ardour, and are almoft every day
G 2. difcoverino-
84 .SUMMARY OF THE PRINCIPAL
difcovering new phenomena, the defcription of which
would employ many hundreds of letters ; nay, per-
haps, I fliould never have done.
^.And here it is I am embarraffed. 1 could not
bear to think of letting you remain unacquainted
with a branch of natural philofophy fo effential j but
I would willingly fave you the fatigue of wading
through a diffufe detail of the phenomena, which,
after all, would not furnifh the neceffary information.
I flatter myfelf, however, that I have difcovered a
road which will lead fo directly to the object, that
you fhall attain a knowledge of it much more per-
fect than that of moll natural philofophers, who de-
vote night and day to the inveftigation of thefe myf-
teries of nature*
Without Hopping to explain the various appear-
ances and effects of electricity, which would engage
me in a long and tedious detail, without extending
your knowledge of the caufes which produce thefe
effects, I fhall purfue quite a different courfe, and
begin with unfolding the true principle of nature on
which all thefe phenomena are founded, however
various they may appear, and from which they are
all eafily deducible.
It is fufficient to remark, in general, that electri-
city is excited by the friction of a glafs tube. It
thereby becomes electrical : and then it alternately
attracts and repels light bodies which are applied to
it, and on the application of other bodies, fparks of
lire are mutually extracted, which, increafed in
itrength, kindle fpirits of wine and other combuftible
fubftances.
PHENOMENA OF ELECTRICITY. 85
fubftances. On touching fuch tube with the finger,
you ' feel, befide the fpark, a puncture which may,
in certain circumftances, be rendered fo acute as to
produce a commotion through the whole body.
Inftead of a tube of glafs, we like wife employ a
globe of the fame, which is made to turn round an
axis, like a turning-wheel. During this motion it
is rubbed with the hand, or with a cufhion applied
to it ; then the globe becomes electric, and produces
the lame phenomena as the tube.
Befides glafs, refinous bodies, fuch as Spanifh wax
and fulphur, likewife poifefs the property of becom-
ing electric by friction ; but certain fpecies of bodies
only have this quality, of which glafs, fealing-wax,
and fulphur, are the principal.
With no effect do other bodies undergo friction ;
no fign of electricity appears : but on applying them
to the nrft, when rendered electric, they immediately
acquire the fame property. They become electric,
then, by communication, as the touch, and frequently
the approximation only, of electric bodies, renders
them fuch.
All bodies, therefore, are divifible into two claries ;
in the one are included fuch as become electric by
friction, in the other thofe which are rendered fuch
by communication, whereas friction produces no
manner of effect on them,. It is very remarkable,
that bodies of the nrft clafs receive no electricity from
communication : when you apply to a tube or globe
of glafs ftrongly electrified, other glafles, or bodies,
which friction renders electric, this touch commu-
G 3 nicates
86 SUMMARY OF THE PRINCIPAL
nicates no electricity to them. The diftinction of
thefe two claifes of bodies is worthy of attention,
the one clafs being difpofed to become electrical by
friction only, and not by communication, the other,
on the contrary, only by communication.
All metals belong to this laft clafs, and the commu-
nication extends fo far, that on preferring one extre-
mity of a wire to an electric body, the other ex-
tremity becomes fo likewife, be the wire ever fo
long ; and on applying ftili another wire to the far-
ther extremity of the firft, the electricity is conveyed
through the whole extent of that fecond thread, and
thus electricity may be tranlinitted to the molt re-
mote diftances.
Water is a fubitance which receives electricity by
communication. Large pools have been electrified
to fuch a degree, that an application of the finger
has elicited fparks, and excited pain.
The prevailing perfuafion now is, that lightning
and thunder are the effect of the electricity which
the clouds acquire, from whatever caufe. A thun-
der ftorm exhibits the fame phenomena of electricity,
on the great fcale, which the experiments of natural
phiiofophers do in miniature.
20tb June, 1761.
LETTER
PHENOMENA OF ELECTRICITY. 87
LETTER XXIV.
The true Principle of Nature, on which are founded all
the Phenomena of Electricity.
THE fummary I have exhibited of the principal
phenomena of electricity, has no doubt excited
a curioiity to know what occult powers. of nature
are capable of producing effects fo furprizing.
The greateft part of natural philofophers acknow-
ledge their ignorance in this refpecl. They appear
to be fo dazzled by the endlefs variety of phenomena
which every day prefent themfelves, and by the An-
gularly marvellous- circumftances which accompany
thefe phenomena, that they are difcouraged from
attempting an inveftigation of the true caufe of them.
They readily admit the exiftence of a fubtile matter,
which is the primary agent in the production of the
phenomena, and which they denominate the electric
fluid ; but they are fo embarraffed about determin-
ing its nature and properties, that this important
branch of phyfics is rendered only more perplexed
by their refearches.
There is no room to doubt, that we muft look
for the fource of all the phenomena of electricity
only in a certain fluid and fubtile matter ; but we
have no need to go to the regions of imagination in
queft of it., That fubtile matter denominated ether ^
whofe reality I have already endeavoured to demon-
G 4 ftrate,
88 ELECTRICITY FOUNDED ON THE
ftrate,* is fuflicient very naturally to explain all the
furprizing effects which electricity prefents. I hope
I fhall be able to fet this in fo clear a light, that you
fhall be able to* account for every electrical pheno-
menon, however itrange an appearance it may af-
fume.
The great requifite is to have a thorough know-
ledge of the nature of ether. The air which . we
breathe rifes only to a certain height above the fur-
face of the earth ; the higher you afcend, the more
fubtile it becomes, and at laft it entirely ceafes. We
muft not affirm, that beyond the region of the air
there is a perfect vacuum, which occupies the im-
menfe fpace in which the heavenly bodies revolve.
The rays of. light which are diffufed in all directions
from thefe heavenly bodies, fufficiently demonftrate
that thofe vaft fpaces are filled with a fubtile matter.
If the rays of light are emanations forcibly pro-
jected from luminous bodies, as fome philofophers
have maintained, it muft follow, that the whole fpace
of the heavens is filled with thefe rays, nay that they
move through it with incredible rapidity. You
have only to recollect the prodigious velocity with
which the rays of the fun are tranfmitfed to us. On
this hypothec's, not only would there be no vacuum,
but all fpace would be filled with a fubtile matter,
ancj that in a. ftate of conftant and moft dreadful
agitation.
But I think I have clearly proved, that rays of
li^ht are no more emanations projected from lumi-
* Vol. I. Letter XV.
nous
TRUE PRINCIPLE OF NATURE. 89
nous bodies, than found is from fonorous bodies. It
is much more certain, that rays of light are nothing
elfe but a tremulous motion or agitation of a fubtile
matter, juft as found confifts of a fimilar agitation
excited in the air. And as found is produced and
tranfmitted by the air, light is produced and tranf-
mitted by that matter, incomparably more fubtile,
denominated ether, which confequently fills the im-
menfe fpace between the heavenly bodies.
Ether then is a medium proper for the tranfmif-
fion of rays of light, and this fame quality puts us in
a condition to extend our knowledge of its nature
and properties. We have only to reflect on the
properties of air, which render it adapted to the re-
ception and tranfmiffion of found. The principal
caufe is its elafticity or fpring. • You know that air
has a power of expanding itfelf in all directions, and
that it does expand, the inftant that obftacles are re-
moved. The air is never at reft, but when its elaf-
ticity is every where the fame; whenever it is greater
in one place than another, the air immediately ex-
pands. We likewife difcover by experiment, that
the more the air is comprefled, the more its elafti-
city increafes : hence the force of air-guns, in which
the air, being very ftrongly compreifed, is capable
of difcharging the ball with aftonifhing velocity. The
contrary takes place when the air is Tarefied : its
elafticity becomes lefs in proportion as it is more ra-
refied, or diffufed over a larger fpace.
On the elafticity of the air, then, relative to its
denfity, depends the velocity of found, which makes
a progrefs
90 OF ELECTRICITY.
a progrefs of about i ooo feet in a fecond. If the
elafticity of the air were increafed, its denfity re-
maining the fame, the velocity of found would in-
creafe : and the fame thing would take place if the
air were more rare, or lefs denfe than it is, its elaf-
ticity being the fame. In general, the more that
any medium, fimilar to air, is elaftic, and at the
fame time lefs denfe, the more rapidly will the agita-
tions excited in it be tranfmitted. And as light is
tranfmitted fo many thoufand times more rapidly
than found, it muft clearly follow, that the ether,
that medium whofe agitations conftitute light, is
many thoufand times more elaftic than air, and, at
the fame time, many thoufand times more rare or
more fubtile, both of thefe qualities contributing to
accelerate the propagation of light.
Such is the reafon which leads to conclude, that
ether is many thoufand times more elaftic and more
fubtile 'than air ; its nature being in other refpecls
fimilar to that of air, in as much as it is likewife a
fluid matter, and fufceptible of compreffion and of
rarefa&ion. It is. this quality which will conduct
us to the explanation of all the phenomena of elec-
tricity.
Z id June, 1761,
LETTER
DIFFERENT NATURE OF BODIES. 91
LETTER XXV,
Continuation, Different Nature of Bodies relatively to
Eleclricity.
ETHER being a fubtile matter, and fimilar to
air, but many thoufand times more rare and
more elaftic, it cannot be at reft, unlefs its elafticity,
or the force with which it tends to expand, be the
fame every where.
As foon as the ether in one place mail be more
elaftic than in another, which is the cafe when it is
more comprefled there, it will expand itfelf into the
parts adjacent, comprefling what it finds there, till
the whole is reduced to the fame degree of elafticity.
It is then in equilibrio ; the equilibrium being no-
thing elfe but the ftate of reft, when the powers
which have a tendency to difturb it counterbalance
each other.
When therefore the ether is not in equilibrio, the
fame thing muft take place as in air, when its equi-
librium is difturbed ; it muft expand itfelf from the
place where its elafticity is greater, toward that where
it is lefs ; but confidering its greater elafticity and
fubtilty, this motion muft be much more rapid than
that of air. The want of equilibrium in the air
produces wind, or the motion of that fluid from
one place to another. There muft therefore be pro-
duced a fpecies of wind, but incomparably more
fubtile, than that of air, when the equilibrium of the
ether
92 DIFFERENT NATURE OF BODIES
ether is difturbed, by which this laft fluid will pafs
from places where it was more compreffed and more
elaftic, to thofe where it Was lefs fo.
This being laid down, I with confidence affirm,
that all the phenomena of electricity are a natural
confequence of want of equilibrium in the ether, fo
that wherever the equilibrium of the ether is dif-
turbed, the phenomena of electricity muft take place ;
confequently, electricity is nothing elfe but a de-
rangement of the equilibrium of the ether.
In order to unfold all the effects of electricity, we
muft attend to the manner in which ether is blended
and inveloped with all the bodies which furround us.
Ether, in thefe lower regions, is to be found only in
the fmall interftices which the particles of the air and
of other bodies leave unoccupied. Nothing can be
more natural than that the ether, from its extreme
fubtilty and elafticity, mould infinuate itfelf into the
fmalleft pores of bodies, which are impervious to air,
and even into thofe of the air itfelf. You will re-
collect that all bodies, however folid they may ap-
pear, are full of pores ; and many experiments in-
conteftibly demonftrate, that thefe interftices occupy
much more fpace than the folid parts ; finally, the
lefs ponderous a body is, the more it muft be filled
with thefe pores, which contain ether only. It is
clear, therefore, that, though the ether be thus dif-
fufed through the fmalleft pores of bodies, it muft
however be found in very great abundance in the
vicinity of the earth.
You will eafily compreIiend9 that the difference
of
RELATIVELY TO ELECTRICITY. 93
of thcfe pores muft be very great, both as to mag-
nitude and figure, according to the different nature
of the bodies, as their diverfity probably depends on
the diverfity of their pores. There muft be, there-
fore, undoubtedly, pores more clofc, and which have
lefs communication with others ; fo that the ether
which they contain is likewife more confined, and
cannot difengage itfelf but with great difficulty,
though its elafticity may be much greater than that
of the ether which is lodged in the adjoining pores.
There muft be, on the contrary, pores abundantly
open, and of eafy communication with the adjacent
pores ; in this cafe it is evident, that the ether lodged
in them can with lefs difficulty difengage itfelf than
in the preceding ; and if it is more or lefs elaftic in
thefe than in the Others, it will foon recover its equi-
librium.
In order to diftinguifh thefe two clafTes of pores,
I fhall denominate the firft clofe, and the others open.
Moft bodies muft contain pores of an intermediate
fpecies, which it will be fufficient to diftinguifh by
the terms more or lefs clofe9 and more or lefs open.
This being laid down, I remark, firft, that if all
bodies had pores perfectly clofe, it would be impof-
fible to change the elafticity of the air contained in
them ; and even though the ether in fome of thefe
pores mould have acquired, from whatever caufe, a
higher degree of elafticity than the others, it would
always remain in that ftate, and never recover its
equilibrium, from a total want of communication.
In this cafe, no change could take place in bodies ;
all
94 DIFFERENT NATURE OF BODIES
all would remain in the fame ftate as if the ether
were in equilibrio, and no phenomenon of electricity
could be produced.
This would likewife be the cafe if the pores of
all bodies were perfectly open : for then, though the
ether might be more or lefs elaftic in fome pores
than in others, the equilibrium would be inftantly
reftored, from the entire freedom of communication,
and that fo rapidly, that we mould not be in a con-
dition to remark the flighteft change. For the fame
reafon, it would be impoffible to difturb the equili-
brium of the ether contained in fuch pores ; as often
as the equilibrium might be difturbed, it would be
as inftantaneoufly reftored, and no fign of electricity
would be difcoverable.
The pores of all bodies being neither perfectly clofe
nor perfectly open, it will always be pollible to dif-
turb the equilibrium of the ether which they con-
tain : and when this happens, from whatever caufe,
the equilibrium cannot fail to re-eftablifh itfelf : but
this re-eftablifhment will require fome time, and this
produces certain phenomena : and you will prefently
fee, much to your fatisfaclion, that they are pre-
cifely the fame which electrical experiments have dis-
covered. It will then appear, that the principles on
which I am going to eftablifh the theory of electri-
city are extremely fimple, and at the fame time ab-
folutely incontrovertible.
2 J to June, 1 76 1.
LETTER
RELATIVELY TO ELECTRICITY. 95
LETTER XXVI.
On the fame Subjecl.
I HOPE I have now furmounted the mod formi-
dable difficulties which prefent themfelves in the
theory of electricity. You have only to prefer ve the
idea of ether, which I have been explaining ; and
which is that extremely fubtile and elaftic matter
diffufed not only through all the void fpaces of the
univerfe, but through the minuteft pores of all bodies,
in which it is fometimes more and fometimes lefs en-
gaged, according as they are more or lefs clofe. This
conlideration conducts us to two principal fpecies of
bodies, of which the one has pores more clofe, and
the other pores more open.
Should it happen, therefore, that the ether con-
tained in the pores of bodies, has not throughout the
fame degree of elafticity, and that it i& more or lefs
comprefled in fome than in others, it will make an
effort to recover its equilibrium ; and it is precifely
from this that the phenomena of electricity take their
rife, which, of confequence, will be varied, in pro-
portion as the pores in which the ether is lodged are
various, and grant it a communication more or lefs
free with the others.
This difference in the pores of bodies perfectly cor-
refponds to that which the firfl phenomena of elec-
tricity have made us to remark in them, by which
fome eafily become electrical by communication, or
1 the
^6 DIFFERENT NATURE OF BODIES
the proximity of an electrical body, whereas others
fcarcely undergo any change. Hence you will im-
mediately infer, that bodies which receive electricity
fo eafily, by communication alone* are thofe whofe
pores are open ; and that the others which are almoft
infenfible to electricity, inuft have theirs clofe, either
entirely or to a very great degree.
It is, then, by the phenomena of electricity them-
felves, that we are enabled to conclude what are the
bodies whofe pores are clofe or open. Reflecting
which permit me tofuggeft the following elucidations*
Firft, the air which we breathe has its pores almoft
entirely clofe ; fo that the ether which it contains^
cannot difengage itfelf but with difficulty, and mull
find equal difficulty in attempting to penetrate into
it. Thus, though the ether diffufed through the air
is not in equilibrio with that which is contained in
other bodies, where it is more or lefs compreffed, the
re-eftablifhment of its equilibrium is not to be pro-
duced without extreme difficulty ; this is to be un-
derftood of dry air, humidity being of a different na-
ture, as I fhall prefently remark.
Farther, we muft rank in this clafs of bodies, with
clofe pores, glafs, pitch, refinous bodies, fealing wax,
fulphur, and particularly filk. Thefe fubftances have
their pores fo very clofe, that it is with extreme dif-
ficulty the ether can either efcape from, or penetrate
into, them.
The other clafs, that of bodies whofe pores are
open, contains, firft, water and other liquors, whofe
nature is totally different from that of air. For this
reafon
RELATIVELY TO ELECTRICITY. 97
reafoh when air becomes humid, it totally changes its
nature with refpect to electricity, and the ether can
enter or efcape without almoft any difficulty. To
this clafs of bodies, with open pores, likewife muff be
referred thofe of animals, and all metals.
Other bodies, fuch as wood, feveral forts of ftones
and earths, occupy an intermediate ftate between the
two principal fpecies which I have juft mentioned,
and the ether is capable of entering or efcaping with
more or lefs facility, according to the nature of each
fpecies.
After thefe elucidations on the different nature of
bodies, with refpect to the ether which they contain,
you will fee with much fatisfaction, how all the phe-
nomena of electricity, which have been confidered as
fo many prodigies, flow very naturally from them.
All depends, then, on the ftate of the ether, dif-
fufedor difperfed through the pores of all bodies, in
as far as it has not throughout the fame decree of
elafticity,' or as it is more or lefs compreffed in fome
than in others ; for the ether not being then in equi-
librio, will make an effort to recover it. It will en-
deavour to difengage itfelf as far as the opennefs of
the pores will permit, from places where it is too
much compreffed, to expand itfelf and enter into
pores where there is lefs compreffion, till it is through-
out reduced to the fame degree of compreffion and
elafticity, and is, of confequence, in equilibrio.
Let it be remarked, that when the ether paffes
from a body where it was too much compreffed, into
another where it is lefs fo, it meets with great ob-
Vol. II. H ftacles
98 DIFFERENT NATURE OF BODIES.
ftacles in the air which feparates the two bodies, on
account of the pores of this fluid, which are almoft
entirely clofe. It however panes through the air, as
a liquid and extremely fubtile matter, provided its
force is not inferior, or the interval between the
bodies too great. Now this paffage of the ether being
very much impeded, and almoft entirely prevented
by the pores of the air, the fame thing will happen
to it, as to air forced with velocity through fmaM
apertures, a hilling found is heard, which proves that
this fluid is then put into an agitation which produces
fuch found.
It is, therefore, extremely natural, that the ether,
forced to penetrate through the pores of the air,
fhould likewife receive a fpecies of agitation. You
will pleafe to recollect,1 that as agitation of the air
produces found, a fimilar agitation of ether produces
light. As often, then, as ether efcapes from one
body, to enter into another, its paffage through the
air muft be accompanied with light ; which appears
fometimes under the form of a fpark,fometimes under
that of a flafh of lightning, according as its quantity
is more or lefs confiderable.
Here, then, is the moft remarkable circumftance
which accompanies moft electrical phenomena, ex-
plained to a demonftration, on the principles I have
laid down. I fhall now enter into a more particular
detail, which will furnifti me with a very agreeable
fubject for fome following letters.
$ztbjme, 1761.
LETTER
OF ELECTRICITY. 99
LETTER XXVII.
Of pofitive and negative Electricity. Explanation of the
Phenomenon of Attraction.
YOU will eafily comprehend from what I have
above advanced, that a body muft become elec-
trical, whenever the ether contained in its pores be-
comes more or lefs elaftic than that which is lodged
in adjacent bodies. This takes place when a greater
quantity of ether is introduced into the pores of
fuch body, or when part of the ether which it con-
tained is forced out* In the former cafe, the ether
becomes more compreffed, and confequently more
elaftic ; in the other, it becomes rarer, and lofes its
elafticity. In both cafes > it is no longer in equilibrio
with that which is external ; and the efforts which
it makes to recover its equilibrium, produce all the
phenomena of electricity.
You fee then that a body may become electric in
two different ways, according as the ether contained
in its pores becomes more or lefs elaftic than that
which is external ; hence refult two fpecies of elec-
tricity : the one, by which the ether is rendered
more elaftic, or more compreffed, is denominated in»
creafed or pofitive eleBricity\ the other, in which the
ether is lefs elaftic, or more rarefied, is denominated
diminijhed or negative eleclricity* The phenomena of*
both are nearly the fame ; a flight difference only is
obfervable, which I fhall mention.
H 2 Bodies
100 OF POSITIVE AND
Bodies are not naturally electrical, as the elafticity
of the ether has a tendency to maintain it in equili-
brio, it muft always require a violent operation to
difturb this equilibrium, and to render bodies elec-
trical; and fuch operations muft act on bodies with
clofe pores, that the equilibrium once deranged may
not be inftantly reftored. We accordingly find that
glafs,. amber, fealing-wax, or fulphur, are the bodies
employed to excite electricity.
The eafieft operation, andj for feme time paft, the
moft universally known, is to rub a flick of fealing
wax, with a piece of woollen cloth, in order to com-
municate to that wax the power of attracting fmall
flips of paper and of other light bodies. Amber, by
means of friction, produces the fame phenomena;
and as the ancients gave to this body the name of
eleflrum,the power excited by friction obtained, and
preferves, the name of ekSiricity : natural philofophers
of the remoteft ages having remarked, that this fub-
ftance acquired by friction the faculty of attracting
light bodies.
This effect undoubtedly arifes from the derange-
ment of the equilibrium of the ether by means of
friction. I muft begin, therefore, with explaining
this well-known experiment. Amber and fealing-
wax have their pores abundantly clofe, and thofe of
wool are abundantly open ; during the friction, the
pores of both the one and the other comprefs them-
felves, and the ether which is contained in them, is
reduced to a higher degree of elafticity. According
as the pores of the wool are fufceptible of a compref-
fion
NEGATIVE ELECTRICITY. l6l
-lion greater or lefs than tliofe of amber or fealing-
wax, it muft happen, that a portion of ether mall
pafs from the wool into the amber, or reciprocally
from the amber into the wool. In the former cafe?
the amber becomes pofitively electric, and in the other
negatively ', and its pores being clofe, it will remain in
this ftate for fome time j whereas the wool, though
it has undergone a fimilar change, will- prefently re-
cover its natural ftate.
From the experiments which electric fealing-wax
furnifhes, we conclude that its electricity is negative;
and that a part of its ether has palled during the
friction into the wool. Hence you perceive how a
ftick of fealing-wax is, by friction on woollen clothe
deprived of part of the ether which it contained, and
muft thereby become electric. Let us now fee what
effects muft refult from this, and how far they cor-
refportd with obfervation and experience.
Let AB (plate II- Jig- 24.) be a ftick of fealing-wax,
from which, by friction, part of the ether contained
in its pores has been forced out ; that which remains
being lefs comprefled, will therefore have lefs force
to expand itfelf, or, in other words, will have lefs
elafticity than that contained in other bodies in
the circumambient air : but as the pores of air are
ftill clofer than thofe of fealing-wax, this prevents
the ether contained in the air from palling into the
fealing-wax, to reftore the equilibrium ; at leaft this
will not take place till after a confiderable interval
of time.
; Let a fmall and very light body C, whofe pores
H 3 are
102 OF POSITIVE AND
are open, be now prefented to the ftick of fealing-wax,
the ether contained in them, finding a free paffage,
becaufe it has more force to expand itfelf than is op-
pofed to it by the ether fhut up in the ilick at c, will
fuddenly efcape, will force a paffage for itfelf through
the air, provided the diftance is not too great, and
will enter into the fealing-wax. This paffage, how-
ever, will not be effected without very confiderable
difficulty, as the pores of the fealing-wax have only
a very finall aperture, and confequently it will not be
accompanied with a vehemence capable of putting
the ether in a motion of agitation, to excite a fenfible
light, A faint glimmer' ng only will be perceptible
jn the dark, if the electricity is fufEciently ftrong.
But another phenomenon will be obfervable, which
is no lefs furprizing, the fmall body C will fpring to-
ward the fealing-wax, as if attracted by it. To ex-
plain the caufe of this, you have only to confider,
that the fmall body C, in its natural ftate, is equally
preffed on all fides by the air which furrounds it ;
but as in its prefent ftate, the ether makes its efcape,
and paffes through the air in the direction C c, it is
evident, that this laft fluid will not prefs fo violently
on the fmall body, on this ftde, than on any other,
and that the preffure communicated to it toward c,
will be more powerful than in any other direction,
impelling it toward the fealing-wax as if attracted
by it.
Thus are explained, in a manner perfectly intel-
ligible, the attractions obfervable in the phenomena
pf electricity. In this experiment, the electricity is
too
NEGATIVE ELECTRICITY. I03
too feeble to produce more furprizing effects. I fhall
have the honour of prefenting you with a more
ample detail in the following letters.
\*b July, 1761.
LETTER XXVIII.
On the fame Subjecl.
SUCH were the faint beginnings of the electrical
phenomena ; it was not till lately that they were
carried much farther. At firft a tube of glafs was
employed, fimilar to that of which barometers are
made ; but of a larger diameter, which was rubbed
with the naked hand, or with a piece of woollen cloth,
and electrical phenomenamore ftrikingwere obferved.
You will readily comprehend, that on rubbing a
tube of glafs, part of the ether muft pafs, in virtue
of the compreflion of the pores of the glafs, and of
the rubbing body, either from the hand into the
glafs, or from the glafs into the hand, according as
the pores of the one or of the other are more fuf-
ceptible of compreflion in the friction. The ether,
after this operation, eafily recovers its equilibrium in
the hand, becaufe its pores are open ; but thofe of
the glafs being abundantly clofe, this fluid will pre-
ferve its ftate in it, whether the glafs were furcharged
or exhaufted, and confequently will be electric, and
will produce phenomena fimilar to thofe of fealing-
wax, but undoubtedly much flronger, as its electri-
city is carried to a higher degree, as well from the
H 4 greater
I04 OF POSITIVE AND /
greater diameter of the tube, as from the very nature
of glafs.
Experiments give us reafon to conclude, that the
tube of glafs becomes, by thefe means, furcharged
with ether, whereas fealing-wax is exhaufted of it 5
the phenomena however are nearly the fame.
It muft be obferved, that the glafs tube retains its
electricity as long as it is furrounded only with air,
becaufe the pores of the glafs and thofe of the air,
are too clofe to allow a communication fufficiently
free to the ether, and to exhauft the glafs of what it
has more than in its natural ftate ; fuperfluity of
ether always increafing elafticity. But the air muft
be very dry, for only when in that ftate are its pores
fufficiently clofe ; when it is humid or loaded with
vapours, experiments do not fucceed, whatever de»
gree of friction you beftow on the glafs. The reafon
is obvious ; for water, which renders the air humid,
having its pores very open, receives every inftant
the fuperfluous ether which was in the glafs, and
which of courfe remains in its natural ftate. Expe-
riments fucceed, then, in only very dry air; let us
now fee what phenomena a glafs tube will, in that
cafe, produce, (plate ILfig* 2 5. ) after having under*
gone confiderable friction.
It is clear, that on prefenting to it a fmall light
body C with open pores, fuch as goldJeaf, the ether
in the tube more elaftic at the neareft parts D, £,
will not make ineffectual efforts to difcharge itfelf
and pafs into the pores of the body C. It will force
a path through the air, provided the diftance be not
too
VcrlJf ^pJi/irui-a£um- oJ*t/z?lfn^/<7'i>so^JJ/aJellJW#7idJe?<<j>js
NEGATIVE ELECTRICITY. 1 05
too great ; and you will even fee a light between the
tube and the body occafioned by the agitation ex-
cited in the ether, which paffes with difficulty from
the tube into the body. When, inftead of the body
C, the finger is applied to it, you feel a pricking oc-
cafioned by the rapid entrance of the ether ; and if
you expofe your face to it at fome diftance, you feel
a certain agitation in the air, excited by the tranfition
of the ether. Thefe circumftances are likewife ac-
companied, fornetimes, with a flight cracking, pro-
duced undoubtedly by the agitation of the air which
the ether traverfes with fuch rapidity.
I muft entreat you to keep in mind, that an agi-
tation in the air always produces a found, and that
the motion of ether produces light ; and then the
explanation of thefe phenomena will become abun-
dantly eafy.
Let the fmall light body C, be replaced in the vi-
cinity of our electric tube; as long as the ether is
efcaping from the tube, to enter into the pores of the
body C, the air will be in part expelled from it, and
confequently will not prefs fo ftrongly on the body
on that fide, as in every other direction ; it will hap-
pen, then, as in the preceding cafe, that the body C
will be impelled toward the tube, and, being light,
will come clofe up to it. We fee, then, that this ap,
parent attraction equally takes place, whether the
ether in the tube be too much or too little elaftic ;
or, whether the elafticity of the tube be pofitive or
negative. In both cafes, the paffage of the ether flops
the air? and by its preffure hinders it from acting.
But
Io6 ON THE ELECTRIC ATMOSPHERE.
But while tjie fmall body C is approaching the
tube, the paflage of the ether becomes ftronger, and
the body C will foon be as much furcharged with ether
as the tube itfelf. Then the action of the ether,
which arifes from its elafticity only, entirely ceafes,
and the body C will fuftain on all fides an equal
preffure. The attraction will ceafe, and the body C
will remove from the tube, as nothing detains it, and
its own gravity puts it in motion. Now as foon as
it removes, its pores being open, its fuperfluous ether
prefently efcapes in the air, and it returns to its na-
tural ftate. The body will then act. as at the begin-
ning, and you will fee it again approach the tube, fo
that it will appear alternately attracted and repelled
by it ; and this play will go on till the tube has loft
its electricity. For as, on every attraction, it dis-
charges fome portion of its fuperfluous ether, befides
the infenfible efcape of part of it in the air, the tube
will foon be re-eftablifhed in its natural ftate, and in
its equilibrium ; and this fo much the more fpeedily
as the tube mall be fmall, and the body C light : then
all the phenomena of electricity will ceafe.
-jib July, 1 761.
LETTER XXIX,
On the eleffric Atmofphere*
I HAD almoft forgot to bring forward a moft ef-
fential circumftance, which accompanies all elec-
tric bodies, whether po/itively or negatively fuch, and
which
ON THE ELECTRIC ATMOSPHERE. I07
which fupplies fome very ftriking elucidations for
explaining the phenomena of electricity.
Though it be indubitably true that the pores of
air are very clofe, and fcarcely permit any communi-
cation between the ether that they contain, and what
is in the vicinity, it undergoes however fome change
when near to an electric body.
Let us firft confider an electric body negatively fo,
as a ftick of fealing-wax v^ B, (plate III. fig. i.) which
has been deprived by friction of part of the ether
contained in its pores, fo that what it now contains
has lefs elafticity than that of other bodies, and con-
fequently than that of the air which furrounds the
wax. It muft neceliarily happen, that the ether con-
tained in the particles of the air which immediately
touch the wax, as at m, having greater elafticity,
{hould difcharge itfelf, in however fmall a degree,
into the pores of the wax, and will confequently lofe
fomewhat of its elafticity. In like manner, the par-
ticles of air more remote, fuppofe at n, will likewife
fuffer a portion of their either to efcape into the nearer
at m, and fo on to a certain diitance, beyond which
the air will no longer undergo any change. In this
manner, the air round the ftick of wax, to a certain
diitance, will be deprived of part of its ether, and be-
come itfelf electric.
This portion of the air, which thus partakes of
the electricity of the ftick of wax, is denominated
the eleclric atmofphere ; and you will fee from the
proofs which I have juft adduced, that every electric
body muft be furrounded with an atmofphere. For
6 if
Io8 ON THE ELECTRIC ATMOSPHERE*
if the body is pofiil-vely eleclric, fo as to contain a Su-
perfluity of ether, it will be more coinpreffed in fuch
a body, and confequently more elaftic, as is the cafe
with a tube of glafs when rubbed; this ether, more
elaftic, then difcharges itfelf, in a fmall degree, into
the particles of air which immediately touch it, and
thence into particles more remote, to a certain dis-
tance ; this will form another- electric atmofphere
round the tube, in which the ether will be more
compreiTed, and confequently more elaftic than elfe-
where.
It is evident that this atmofphere which furrounds
fuch bodies, muft gradually diminifh the electricity
of them, as in the firft cafe there paffes almoft con-
tinually a fmall portion of ether, from the furround*
ing air, into the eleclric body, and which, in the
other cafe, iiTues from the electric body, and paffes
into the air. This is likewife the reafon why electric
bodies at length lofe their electricity ; and this fd
much the fooner, as the pores of the air are more
open. In a humid air, whofe pores are very open,
all electricity is almoft inftantly extinguiihed ; but
in very dry air it continues a confiderable time.
This electric atmofphere becomes abundantly fen-
iible, on applying your face to an electrified body ;
you have a feeling fimilar to the application of a fpi-
der's web, occafioned by the gentle tranfition of the
ether from the face into the electric body, or red*
procally from this laft into the face, according as it
is negative or pofitive, to ufe the common expreffion.
The electric atmofphere ferves likewife more clearly
to
ON THE ELECTRIC ATMOSPHERE. 109
to explain that alternate attraction and repulfion of
light bodies placed near to electric bodies, which I
mentioned in the preceding letter ; in which you
muft have remarked, that the explanation of repul-
fion, there given, is incomplete ; but the electric at-
mofphere will fupply the defect.
• Let A B (plate III. Jig. 2. J reprefent an electric
tube of giafs furcharged with ether, and let C be a
fmall light body, with pores fufficiently open, in its
natural flate. ; Let the atmofphere extend as far as
the diftance D E. Now, as the vicinity of C con-
tains already an ether more elaftic, this will difcharge
itfelf into the- pores of the body C, there will imme-
diately iflue from the tube a new ether, which will
pafs from D into C, and it is the atmofphere chiefly
which facilitates this paffage. For if the ether con-
tained in the air had no communication with that in
the tube, the corpufcle C would not feel the vicinity
of the tube ; but while the ether is paiTmg from D
to Q, the preifure of the air between C and D will
be diminiihed, and the corpufcle C will no longer be
preffed equally in all directions ; it will therefore be
impelled toward D, as if attracted by it. Now in
proportion as it approaches, it will be likewile more
and more furcharged with ether, and will become
electric as the tube itfelf, and, consequently, the elec-
tricity of the tube will no longer act upon it.
But as now the corpufcle, being arrived at D, con-
tains too much ether, and more than the air at E, it
will have a tendency to efcape, in order to make its
way to E. The atmofphere, in which the compref-
fion
110 ON THE ELECTRIC ATMOSPHERE*.
fion of the ether continues to diminifli from DtoE
will facilitate this paflage, and the fuperfluous ether
will in effect flow from the corpufcle toward E. By
this paflage, the preffure of the air on the corpufcle
will be fmaller on that lide than every where elfe,
and confequently the corpufcle will be carried to*
ward D, as if the tube repelled it. But as foon as it
arrives at £, it difcharges the fuperfluous ether, and
recovers its natural ftate ; it will then be again at-
tracted toward the tube, and, having reached it, will
be again repelled, for the reafon which I have juft
been explaining.
It is the electric atmofphere then, chiefly, which
produces thefe Angular phenomena, when we fee
electrified bodies alternately attract and repel fmafl
light bodies, fuch as little flips of paper, or particles
of metal, with which this experiment beft fucceeds,
au the fubftances have very open pores.
You will fee, moreover, that what I have juft now
faid refpecting pofitive electricity, muft equally take
place in negative. The tranfition of the ether is only
reverfed, by which the natural preffure of the air
muft always be diminifhed.
llth July, 1 76 1.
LETTER
COMMUNICATION OF ELECTRICITY. Ill
LETTER XXX.
Communication of Eleclricity to a Bar of Iron, by meant
of a Globe of Glafs.
AFTER the experiments made with glafs tubes,
we have proceeded to carry electricity to a
higher degree of ftrength. Inftead of a tube, a globe,
or round ball of glafs, has been employed, which is
made to turn with great velocity round an axis, and
on applying the hand to it, or a cufhion of fome
matter with open pores, a friction is produced,
which renders the globe completely electric.
Figure 4. of plate III. reprefents this globe, which
may be made to move round an axis A B, by a me-
chanifm fimilar to that employed by turners. C is
the cufhion flrongly applied to the globe, on which
it rubs as it turns round. The pores of the cufhion
being, in this friction, compreifed more than thofe
of the glafs, the ether contained in it is expelled,
and forced to infinuate itfelf into the pores of the
glafs, where they continue to accumulate, becaufe
the open pores of the cufhion are continually fupply-
ing it with more ether, which it is extracting, at
leaft in part, from furrounding bodies ; and thus the
globe may be furcharged with ether to a much higher
degree than glafs tubes. The effects of electricity
are, accordingly, rendered much more confiderable,
but of the fame nature with thofe which I have de-
fcribed, alternately attracting and repelling light bo-
dies -f
112 COMMUNICATION OF ELECTRICITY.
dies ; and the fparks which we fee, on touching the
electric globe, are much more lively.
But naturalifts have not refted fatisfied with fuch
experiments, but have employed the electrical globe
in the difcovery of phenomena much more fur-
prizing.*
Having conitructed the machine for turning the
globe round its axis AB, a bar of iron FG is fuf-
pended above, or on one fide of, the globe, and to-
ward the globe is directed a chain of iron or other
metal ED, terminating at D, in metallic filaments,
which touch the globe. It is fufficient that this
chain be attached to the bar of iron in any manner
whatever, or but touch it. When the globe is turned
round, and, in turning, made to rub on the cufiiion
at C, in order that the glafs may become furcharged
with ether, which will, confequently, be more elaftic,
it will eafily pafs from thence into the filaments D,
for, being of metal, their pores are very open ; and
from thence, again, it will difcharge itfelf by the
chain DE, into the bar of iron FG. Thus by means
of the globe, the ether extracted from the cuiliion C,
will fuccefiively accumulate in the bar of iron FG,
which likewife, of confequence, becomes electric,
and its electricity increafes in proportion as you con-
tinue to turn the globe.
If this bar had a farther communication with
other bodies, whofe pores too are open, it would
foon difcharge into them its fuperfluous ether, and
thereby lofe its electricity ; the ether extracted from
* See Plate III. Fig. 3.
the
TO A BAR OF IRON. II3
the cufhion would be difperfed over all the bodies
which had an inter-communication, and its greateft
compreflion would not be more perceptible. To
prevent this, which would prove fatal to all the phe-
nomena of electricity, the bar muft, of neceflity, be
fupported, or fufpended, by props of a fubftance
whofe pores are very clofe ; fuch are glafs, pitch,
fulphur, fealing-wax, and filk. It would be proper,
then, to fupport the bar on props of glafs or pitch ;
- or to fufpend it by cords of filk. The bar is thus
fecured as;ainft the tranfmifiion of its accumulated
ether, as it is furroundecl on all fides only by bodies
with clofe pores, which grant hardly any admiffion
to the ether in the bar. The bar is then faid to be
ifolated, that is, deprived of all contact which could
communicate, and thereby diminiih, its electricity.
You muft be fenfible, however, that it is not poffible
abfolutely to prevent all wafte ; for this reafon the
electricity of fuch a bar muft continually diminiih,
if it were not kept up by the motion of the globe.
In this manner electricity may be communicated
to a bar of iron, which never could be done by the
moft violent and perfevering friction, became of the
opennefs of its pores. And, for the fame 'reafon,
fuch a bar rendered electric by communication, pro-
duces phenomena much more furprizing. On pre-
senting to it a finger, or any other part of the body,
you fee a very brilliant fpark dart from it, which,
entering into the body, excites a pungent, and fome-
times -painful, fenfation. I recollect my once having
prefented to it my head? covered with my peruke and
Vol. H. I hat,
H4 Communication of electricity.
hat, and the ftroke penetrated it fo acutely, that I
feit the pain next day.
Thefe fparks, which efcape from every part of the
bar, on prefcnting to it a body with open pores, let
on fire, at once, fpirit of wine, and kill fmall birds
whofe heads are expofed to them. On plunging
the end of the chain DE into a bafon filled with
water, and fupported by bodies with clofe pores, fuch
as glafs, pitch, filk, the whole water becomes electric;
and fome authors affure us that they have feen con-
liderable lakes electrified in this manner, fo that, on
applying the hand, you might have feen even very
pungent fparks emitted from the water. But it ap-
pears to me, that the globe muft be turned a very
long time indeed, to convey fuch a portion of ether,
into a mafs of water fo enormous; it would be like-
wife neceffary that the bed of the lake, and every
thing in contact with it, fliould have their pores
clofe.
The more open, then, the pores of a body are?
the more difpofed it is to receive a higher degree of
electricity, and to produce prodigious effects. You
muft admit that all this is perfectly conformable to
the principles which I at firft eltablifhed.
i^tb July, 1 76 1.
LETTER
ELECTRISATION OF ANIMALS. 115
LETTER XXXI.
Eleftrifation of Men and Animals.
AS electricity may be communicated from glafs
to a bar of iron, by means of a chain, which
forms that communication, it may likewife be con-
veyed into the human body; for the bodies of ani-
mals have this property in common with metals and
water, that their pores are very open ; but the man,
who is to be the fubjecr. of the experiment, muft not
be in contact with other bodies whofe pores are like-
wife open.
For this effect, the man is placed on a large lump
of pitch, or feated on a chair fupported by glafs co-
lumns, or a chair fufpended by cords of filk, as all
thefe fubftances have pores fufficiently clofe to pre-
vent the efcape of the ether, with which the body of
the man becomes furcharged by electricity.
This precaution is abfolutely neceiTary, for were
the man placed on the ground, the pores of which
are abundantly open, as foon as the ether was con-
veyed into his body, to a higher degree of compref-
lion, it would immediately difcharge itfelf into the
earth, and we muft be in a condition to furcharge it
entirely with ether, before the man could become
electric. Now you muft be fenfible, that the cufhion
by which the globe of glafs is rubbed, could not pof-
fibly fupply fuch a prodigious quantity of ether, and
that were you to extract it even out of the earth it-
I % felf,
Il6 ELECTRISATION OF
felf, you could gain no ground, for you would juft
take away as much on the one hand as you gave on
the other.
Having, then, placed the man, whom you mean
to electrify, in the manner which I have indicated,
you have only to make him touch, with his hand,
the globe of giafs while it turns, and the ether, ac-
cumulated in the globe, will eahly pafs into the open
pores of the hand, and diffufe itfelf over the whole
body, from whence it cannot fo eafily efcape, as the
air, and all the bodies with which he is furrounded,
have their pores clofe. Inilead of touching the globe
with his hand, it will be fumcient for him to touch
the chain, or even the bar, which I defcribed in the
preceding letter ; but in this cafe, not only the man
himfelf muft be furcharged with ether, but likewife
the chain with the bar of iron ; and as this requires
a greater quantity, of ether, it would be neceilary to
labour longer in turning the globe, in order to fup-
ply a fuhicient quantity.
In this manner the man becomes entirely, electric,
or, in other words, his whole body will be fur-
charged with ether, and this fluid will confequently
be found there in the highefl degree of comprefiion
and electricity, and will have a violent tendency to
efcape.
You muft be abundantly fenfible, that a ftate fo
violent cannot be indifferent to the man. The body
is, in its minuteft parts, wholly penetrated with
ether, and the fmalleft fibres, as well as the nerves,
are fo filled with it, that this ether, without doubt
pervades
MEN AND ANIMALS. l\J
pervades the principal fprings of animal and vital -
motion. It is, accordingly, obferved, that the pulfe
of a man electrified beats fafter, he is thrown into a
fweat, and the motion of the more fubtile fluids,
with which the body is filled, becomes more rapid.
A certain change is likewife felt over the whole
bedy, which it is impoiTible to defcribe ; and there
is every reafon to believe, that this ftate has a pow-
erful 'influence on the health, though fufficient ex-
periments have not yet been made, to afcertain in
what cafes this influence is falutary or otherwife. It
may fometimes be highly beneficial to have the blood
and humours raifed to a more lively circulation ;
certain obftruclions, which threaten dangerous con-
fequences, might thereby be prevented ; but on other
occafions, an agitation too violent might prove in-
jurious to health. The fubjecT: certainly well deferves
the attention of medical gentlemen. We have heard
of many furprizing cures performed by electricity,
but we are not yet enabled fufficiently to diftinguifh
the/ occafions on which we may promife ourfelves
fuccefs.
To return to our electrified man ; it is very re-
markable that, in the dark, we fee him furrounded
with a light, fimilar to that which painters throw
round the heads of faints. The reafon is abundantly !
obvious j as there is always efcaping from the body
of that man, fome part of the ether with which he
is furcharged, this fluid meets much refiftance from
the clofe pores of the air, it is thereby put into a
J 3 ' certain
1 1 8 ELECTRISATION OF ANIMALS.
certain agitation, which is the origin of light, as I
have had the honour to demonftrate.
Phenomena of a very furprizing nature are re*
marked, in this ftate of a man electrified. On touch-
ing him, you not only fee very brilliant fparks iffue
from the part which you touch, but the man feels,
befides, a very pungent pain. Farther, if the per-
fon who touches him be in his natural ftate, or not
•electrified, both fenfibly feel this pain, which might
have fatal confequences, efpecially if he were touched
in the head, or any other part of the body of acute
fenlibility. You will readily comprehend, then, how
little indifferent it is to us, that part of the ether
contained in our body efcape from it, or that new
ether is introduced, efpecially as this is done with
fuch amazing rapidity.
Moreover, the light, with which we fee the man
furrounded in the dark, is, an admirable confirmation
of my remarks refpecting the electric atmofphere
which is diffufed round all bodies ; and you will no
longer find any difficulty in the moft part of elec-
trical phenomena, however inexplicable they may,
at firft, appear.
LETTER
SPECIES OF ELECTRICITY. II9
LETTER XXXII.
D'ljlin&ive Char after of the two Species of Eleclriclty.
YOU will pleafe to recoiled, that not only glafs
becomes electric by friction, but that other fub-
ftances, fuch as fealing-wax and fulphur, have the
fame property, in as much as their pores are likewife
clofe, fo that whether you introduce into them an ex-
traordinary quantity of ether, or extract a part of
it, they continue for fome time in that Hate, nor is
the equilibrium fo foon reftored.
Accordingly, inftead of a globe of glafs, globes of
fealing-wax and fulphur are employed, which are
likewife made to revolve round an axis, rubbing at
the fame time againft a cufhion, in the fame manner
which I defcribed reflecting a globe of glafs. Such
globes are thus rendered equally electric, and, on ap-
plying to them a bar of iron which touches them
only by flender filaments or fringes of metal, inca-
pable of injuring the globe, electricity is immediately
communicated to that bar, from which you may
afterwards tranfmit it to other bodies at pleafure.
Here, however, a very remarkable difference is
obfervable. A globe of dafs rendered electric in
this manner, becomes furcharged with ether, and
the bar of iron, or other bodies brought into com-
munication with it, acquire an electricity of the fame
nature ; or, in other words, the ether contained is in
a ftate of too great compreffion, whofe elafticity is
1 4 increafed*
120 CHARACTER OF THE TWO
increafed. This electricity is denominated pefttive or
augmented electricity. But when a globe of fealing-
wax or fulphur is treated in the fame manner ; an
eleclricity directly oppoiite is the refult, which is de-
nominated negative, or diminijhed eleclricity, as it is
perceived that, by friction, thefe globes are deprived
of part of the ether contained in their pores.
You will be lurprized to fee that the fame friction
is capable of producing effects altogether oppoiite;
but this depends on the nature of the bodies which:
undergo the friction, whether by communicating or
receiving it, and of the rigidity of their particles
which contain the pores. In order to explain the
poffibility of this difference, it is evident, at firfl
fight, that when two bodies are rubbed violently
againfl each other, the pores of the one mull, in mofl
cafes, undergo a greater compreffion than thofe of
the other, and that then, the ether contained in the
pores, is extruded, and forced to infinuate itfelf into
thofe of the bodies which are lefs compreffed.
It follows, then, that in this friction of glafs againfl
a cufhion, the pores of the cufhion undergo a greater
compreffion than thofe of the glafs, and confequently
the ether of the cufhion mufl pafs into the glafs, and
produce in it a pofitive or increafed electricity, as I
have already fliewed. But on fubflituting a globe
of fealing-wax or of fulphur in place of the glafs, thefe
fubflances being fufceptible of a greater degree of
pompreffion in their pores,, than the fubftance of the
cufhion with which the friction is performed, a part
of the ether contained in thefe globes will be forced
out,
SPECIES OF ELECTRICITY. 121
out, and conftrained to pais into the cufhion ; the
globe of fealing-wax or fulphur will, thereby, be de-
prived of part of its ether, and, of courfe, receive a
negative or dimi?iijhed electricity.
. The electricity which a bar of iron, or of any other
metal, receives from communication with a globe of.
fealing-wax or fulphur, is of the fame nature ; as is
alfo that which is communicated to a man placed on
a lump of pitch, or fufpended by cords of filk. When
fuch a man, or any other body, with open porer.,
electrified in the fame manner, is touched, nearly the
fame phenomena are obfervable, as in the cafe of po-
fitive electricity. The touch is here likewife accom-
panied with a fpark, and a puncture on both fides.
The reafon is obvious : for the ether which, in this
cafe, efcapes from bodies in their natural ftate, to
enter into electrified bodies, being under conftraint,
muft be under an agitation, which produces light. A
' fenfible difference is, however, to be remarked in the
figure of the fpark, according as the electricity is po-
fitive or negative. See that of pofitive electricity ; .
plate HI. fig. 5. '
If the bar A B poffeffes pofitive electricity, and the
finger C is prefented to it, the light which ifhies out
of the bar appears under the form of rays diverging
from the bar toward the finger m n> and the luminous
point is feen next the finger.
But if the bar A B (plate III. Jig* 6. J is negatively
electric, and the finger C is prefented to it, the lu-
minous rays m n diverge from the finger, and you
fee the luminous point p next the bar.
This
*22 OF THE TWO SPECIES '
This is the principal character by which pofitive
is diftinguifhed from negative electricity. From
whence foever the ether efcapes, the fparkis emitted
in the figure of rays diverging from that point ; but
when the ether enters into a body, the fpark is a lu-
minous point toward the recipient body.
Zijl July, l76i.
LETTER XXXIII.
How the fame Globe- of Glafs may ftrnifh, at once, the
two Species of Eleclricily.
YOU will be enabled to fee ftill more clearly the
difference between pofitive and negative electri-
city, after I have explained how it is poffible to pro-
duce, by one and the fame globe of glafs, both the
fpccies ; and this will ferve, at the fame time, farther
to elucidate thefe wonderful phenomena of nature.
Let A B ( 'plate VI* jig* \-J be the globe of4 glafa,
turning round its axis C, and rubbed againft by the
cufhion D, in an oppofite direction to which the
globe is touched by the metallic filaments F, attached
to the bar of iron FG, which is fufpended by cords
of filk H and I, that it may no where touch bodies
with open pores.
This being laid down, you know that, by friction
againft the cufhion D, the ether paffes from the
cufhion into the glafs, from which it becomes more
compreffed, and confequently more elaftic : it will
pais, therefore, from thence, by the metallic filaments
F, into
Vol.JT.
JPIaiein
Fw,l
-JZ#T2
OF ELECTRICITY. I 23
E, into the bar of iron F G : for though the pores
of glafs are abundantly clofe, as the ether in the globe
is continually" accumulating by the friction, it foon
becomes fo overcharged, that it efcapcs by the metallic
filaments; and difcharges itfelf into the bar, by which
this laft becomes equally electric.
Hence you perceive, that all this fuperfluity of ether
is fupplied by the cufhion, which would fpeedily be
exhausted, unlefs it had a free communication with
the frame which fupports the machine, and thereby
with the whole earth which is every inflant fupplying
the cufhion with new ether, fo that as long as the
friction continues, there is a quantity fufficient farther
to comprefs that which is in the globe and in the bar.
But if the whole machinery is made to reft on pillars
of glafs, as M and N, or if it is fufpended by cords of
fiik, that the cufhion may have no communication
with bodies whofe pores are open, which might fupply
the deficiency of ether, it would foon be exhaufted,
and the electricity could not be conveyed into the
globe and the bar, beyond a certain degree, which
will be fcarcely perceptible, unlefs the cufhion be of
a prodigious fize. To fupply this defect, the cufhion
D is put in communication with a large mafs of metal
E, the ether of which is fufficient to fupply the globe
and the bar, and to carry it to fuch a high degree of
compreffion.
You will thus procure to the globe and to the bar
a pofitive electricity, as has been already explained.
But in proportion as they become furcharged with
ether, the cufhion and the metallic mafs E will lofe
the
124 - . SPECIES OF ELECTRICITY.
the fame quantity, and thereby acquire a negative
electricity : fo that we have here, at once, the two
fpecies of electricity ; the pofitive in the bar, and the
negative in the metallic mafs. Each produces its
effect conformably to its nature. On prefenting a
finger to the bar, a fpark with divergent rays will
hTue from the bar, and the luminous point will be
feen toward the finger ; but if you prefent the finger
to the metallic mafs, the fpark with divergent rays
will iffue from the finger, and you will fee the lumi-
nous point toward the mafs.
Let us fuppofe two men placed on lumps of pitch,
to cut off all communication between them and bodies
with open pores : let the one touch the bar, and the
other the metallic mafs, while the machine is put in
motion j it is evident that the former will become
pofitively electric, or furcharged with ether, whereas
the other, he who touches the metallic mafs, will ac-
quire a negative eleclricity, and lofe his ether.
Here then are two electric men*, but in a manner
totally different, though rendered fuch by the fame
machine. Both will be furrounded by an electric
atmofphere, which, in the dark, will appear like the
light that painters throw about the figures of faints.
The reafon is, that the fupc.rfluous ether of the one
Infenfibly efcapes into the circumambient air ; and
"that, with refpect to the, other, the ether contained in
the air infenfibly infinuates itfelf into his body. This
tranfition, though infenfible3 will be accompanied,
with an agitation of ether, which produces light. 'B.
It is evident that thefe two fpecies of electricity arex
directly
THE LBYXJEN EXPERIMENr. 1 25
directly oppofite ; but in order to have a thorough
conviction of it, let thefe two join hands, or only
touch each other, and you will fee very vehement
fparks iffue from their bodies, and they themfelves
will feel very acute pain.
If they were electrified in the fame manner, which
would be the cafe if both touched the bar or the me-
tallic mafs, they might fafely touch each other ; no
fpark, and no pain, would enfue, becaufe the ether
contained in both would be in the fame ftate ; whereas
in the cafe laid down, their ftate is directly oppofite.
zybjuly, 1 76 1.
LETTER XXXIV.
The Ley den Experiment.
NOW proceed to defcribe a phenomenon of elec-
tricity 5 which has made a great deal of noife, and
which is known by the name of the Leyden experiment,
becaufe Mr. Moufchenbroeck, profeiTor at Leyden, is
the inventor of it. What is moft aftonifhins; in this
experiment, is the terrible ftroke refulting from it,
by which feveral pcrfons at once may receive a very
violent mock.
Let C be a globe of glafs, turned round by means
of the handle E, and rubbed by the cufhion D D,
which is preffed upon the globe by the fpring O.
At Q are the metallic filaments, which tranfmit the
electricity into the bar of iron F G, by the metallic
chain P.
6 Hitherto
126 THE LEYDEN EXPERIMENT.
Hitherto there is nothing different from the pro-
cefs already defcribed. But in order to execute the
experiment in queftion, to the bar is attached ano-
ther chain of metal H, one extremity of which I, is
introduced into a glafs-bottle K K, filled with water;
the bottle too is placed in a bafon L L, likewife filled
with water. You plunge, at pleafure, into the water
in the bafon another chain A, one end of which
dra^s on the floor.
Having put the machine in motion for fome time,
that the bar may become fufliciently electric, you
know- that: if the finger were to be prefented to the
extremity of the bar at #, the ufual flroke of elec-
tricity would be felt, from the fpark iffuing out of it.
But were the fame peifon, at the fame time, to put
the other hand into the w?_ter in the bafon at A, of
were he but to touch with any part of his body the
chain plunged in that water, he would receive a
ftroke incomparably more violent, by which his
whole frame would undergo a fevere agitation.
This fiiock may be communicated to many p'er-
fons at once. They have only to join hands, or to
touch each other were it but by the clothes ; then
the firft puts his hand into the water in the bafon,
or touches the chain only, one end of which is
plunged into it, and as foon as the laftperfon applies
his finger to the bar, you will fee a fpark dart from it
much more vehement than ufual, and the whole
chain of perfons feel, at the fame inftant, a very vio-
lent fhock over their whole body.
Such is the famous Leyden experiment, which is
fa
THE I.EYDEN EXPERIMENT. \2*J
ib much the more furprizing, that it is difficult to
fee how the bottle, and the water in the bafon, con-
tribute to increafe fo confiderably the effect, of the
electricity. To folve this difficulty, permit me to
make the following reflections.
r.
While, by the action of the machine, the ether is
compreffed in the bar, it paries by the chain H into
the water contained in the bottle I, and there meet-
ing a body with open pores, the water in the bottle
will become as much furcharged with ether as the
bar itfelf.
II.
The bottle, being glafs, has its pores clofe, and
therefore permits not the ether, compreffed within it,
to pierce through the fubfeance of the glafs, to dis-
charge itfelf into the water in the bafori ; confe-
quently the water in the bafon remains in its natural
ilate, and will not become electric ; or even on the
luppoiition that a little of the ether might force its
way through the glafs, it would prefently be loft in
the bafon and pedeftal, the pores of which are open.
III.
Let us now conlider the cafe of a man with one
hand in the water in the bafon, or only in contact
with the chain A, one extremity of which is in>
merfed in that water ; let him prelent the other hand
to the bar at a, the refult will be, as the hrft effect,
that with the fpark which iffues from the bar, the
ether will make its efcape with great velocity, and
meeting
£2iS THE LEYDEN EXPERIMENT.
meeting every where, in the body of the man, open
pores, will without obilruction be diffufed over it.
IV.
Hitherto we fee only the ufual effect of electricity ;
but while the ether with fuch rapidity flies over the
body of the man, it difcharges itfelf with equal ra-
pidity, by the other hand, or by the chain A, into
the water in the bafon ; and as it enters this with
fuch impetuofity, it will eaiily overcome the obflacle
oppofed by the glafs, and penetrate into the water
which the bottle contains.
V.
Now the water in the bottle containing already an
ether too much compreffed j it will acquire, from
this increafe, new force, and will diffufe itfelf with
impetuofity as well through the chain I H, as through
the bar itfelf : it will, of confequence, make its efcape
thence at a with new efforts ; and as this is per-
formed in an inftant, it will enter into the finger
with increafed force, to be diffufed over the whole
body of the man.
VI.
Pafilng thence a-new into the water in the bafon,
and penetrating the bottle, it will increafe ftill farther
the agitation of the ether compreffed in the water
of the bottle, and in the bar ; and this will continue
till the whole is reftored to equilibrium, which will
quickly take place, from the great rapidity with which
the ether acts.
VII. The
*
VoiJT.
-l/aie
NATURE OF ELECTRICITY. 120.
VII.
The fame thing will happen if you employ fevcral
perfons inftead of one man. And now, I flatter my-
felf, you fully comprehend whence arifes the furpriz-
ing increafe of force in the electricity which is pro-
duced by this experiment* of Mr. Moufchenbroeck^ and
which exhibits effects fo prodigious.
VIII.
If any doubt could remain refpecHng what I have
advanced, that the ether compreifed in the water of
the bottle could not penetrate through the glafs, and
that afterwards I have allowed it a palfage abundantly
, free ; fuch doubt will vanifh. when it is confidered,
that, in the firft cafe, every thing is in a ftate of tran-
quillity, and, in the laft, the ether is in a terrible agi-
tation, which muft undoubtedly aflift its progrefs
through the clofeft palfages.
1%th July, 1761.
LETTER XXXV.
Reflections on the Caufe and Nature of 'Electricity ', and on
other Means proper to produce it,
AFTER thefe elucidations, you can be at no lofs
refpecling the caufe of the prodigious effects
obfervable in the phenomena of electricity.
Moll authors who have treated the fubject, per-
plex the experiments in fuch a manner, that they are
rendered abfolutely unintelligible, efpecially when
they attempt an explanation. They have recourfe to
Vol. II. K a certain
13"° 0N THE CAUSE ANt)
a certain fubtile matter which they denominate the
eledric fluid, and to which they afcribe qualities fo ex-
travagant that the mind rejects them with contempt ;
and they are conftrained to acknowledge, at length,
that all their efforts are infufficient to furnifh us with
a folid knowledge of thefe important phenomena of
nature.
But you are enabled to conclude, from the prin-
ciples which I have unfolded, that bodies evidently
become electric, only fo far as the elafticity, or the
ftate of the compreflion of the ether in the pores of
bodies, is not the fame as every where elfe ; in other
words, when it is more or lefs compreffed in fome
than in others. For, in that cafe, the prodigious
elafticity with which the ether is endowed, makes
violent efforts to recover its equilibrium, and to re-
ft ore every where the fame degree of elafticity, as
far as the nature of the pores, which, in different
bodies, are more or lefs open, will permit ; and it is
the return to equilibrium which always produces the
phenomena of electricity.
When the ether efcapes from a body where it is
more compreffed, to difcharge itfelf into another
where it is lefs fo, this paffage is always obftructed by
the clofe pores of the air ; hence it is put into a cer-
tain agitation, or violent motion of vibration, in
which, as we have feen, light confifts ; and the more
violent this motion is, the more brilliant the light
becomes, till it becomes at length capable of fetting
bodies on fire, and of burning them.
While the ether penetrates the air with fo much
force,
NATURE OF ELECTRICITY. 131
force, the particles of air are likewife put into a mo-
tion of vibration, which occaiions found ; it is ac-
cordingly obferved, that the phenomena of electricity
are accompanied with a cracking noife, greater or
lefs, according to the diverfity of circumftances.
And as the bodies of men and animals are filled
with ether in their minuteft pores, and as the action
of the nerves feems to depend on the ether contained
in them, it is impoffible that men and animals fhould
be indifferent with refpect to electricity; and when
the ether in them is put into a great agitation, the
effect muff be very fenfible, and, according to cir-
cumftances, fometimes falutary, and fometimes hurt-
ful. To this laft clafs, undoubtedly, muft be referred
> the terrible ftiocks of the Leyden experiment ; and
there is every reafon to believe that it might be car-
ried to a degree of force capable of killing men, for,
by means of it, many fmall animals, fuch as mice
and birds, have actually been killed.
Though friction ufually is employed in the pro-
duction of electricity, you will eafily comprehend,
that there may be other means befides this. What-
ever is capable of carrying the ether contained in the
pores of a body to a greater or lefs degree of com-
preflion than ordinary, renders it eleftric ; and if it's
pores are clofe, there the electricity will be of fome
duration ; whereas in bodies whofe pores are open,
it cannot poffibly fubfift, unlefs furrounded by air,
or other bodies with clofe pores.
Hence it has been obferved, that heat frequently
K 2 fupplies
I32 NATURE OF ELECTICITY.
fupplies the place of friction. When you heat or
melt fealing-wax, or fulphur, in a fpoon, you dif-
cover a very fenfible electricity in thefe fubftances,
after they are cooled. The reafon is no* longer a
myftery, as we know that heat enlarges the pores of
all bodies, for they occupy a greater fpace when hot
than when they are cold.
You know that, in a thermometer, the mercury^
rifes in heat, and falls in cold ; becaufe it occupies a
greater fpace when it is hot, and fills the tube more
than when it is cold. We find, for the fame reafon,
that a bar of iron very hot is always fomewhat longer
than when cold ; a property common to all bodies
with which we are acquainted.
When, therefore, we melt, by fire, a mafs of feal-
ing-wax, or fulphur, their pores are enlarged, and
probably more open ; a greater quantity of ether
muft, of courfe, be introduced to fill them. When,
afterwards, thefe fubftances are fuffered to cool, the
pores contract and clofe, fo that the ether in them
is reduced to a fmaller fpace, and confequently car-
ried to a higher degree of comprellion, which in-
creafes it's elafticity : thefe maftes will acquire, there-
fore, a pofitive electricity, and muft confequently
exhibit the effects of it.
This property of becoming electric by heat is re-
marked in moft precious ftones. Nay there is aftone
found in Ceylon, named Tourmalin, which, rubbed
or heated, acquires at once the two fpecies of elec«
tricity. The ether in one part of the ftone is ex-
pelled'
NATURE OF THUNDER. I33
pelled, to comprefs more that which is in the other
part ; and its pores are too clofe to permit the re-
eftablifhment of the equilibrium.
\Ji Augnfiy 1 76 1.
LETTER XXXVI.
Nature of Thunder : Explanations of the ancient Phi-
lofophers, and of Defcartes : Refemblance of the Phe-
nomena of Thunder ; and thofe of Eleclricity.
1HAVE, hitherto, conlidered electricity only as an
object of curiofity and {peculation to naturalifts :
but you will prcfently fee, not without fome degree
of furprize, that thunder and lightning, as well as
all the terrible phenomena which accompany them,
derive their origin from the fame principle ; and
that in thefe, nature executes, on the great fcale, what
naturalifts do in miniature, by their experiments.
Thofe philofophers, who thought they faw fome
refemblance between the phenomena of thunder and
thofe of electricity, were at firft conlidered as vi-
fionaries ; and it was imagined that they made ufe
of this pretence merely as a cover to their ignorance
reflecting the caufe of thunder ; but you will foon
be convinced, that every other explanation of thefe
grand operations of nature is deftitute of foundation.
In truth, every thing advanced on the fubjecT:, pre-
vious to the knowledge of electricity, was a mafs of
abfurdity, and little calculated to convey inftruction
refpecting any, the leaft, phenomena of thunder.
K -5 Ancient
134 NATURE OF THUNDER.
Ancient philofophers attributed the caufe of it tq
fulphureous and bituminous vapours, which, afcend-
ing from the earth into the air, mixed with the
clouds, where they caught fire, from fome unknown
caufe.
Defcartes, who quickly perceived the infufficiency
of this explanation, imagined another caufe in the
clouds themfelves, and thought that thunder might
be produced by the fudden fall of more elevated
clouds, on others in a lower region of the air ; that
the air, contained in the intermediate fpace, was
comprefTed by this fall, to fuch a degree as was ca-
pable of exciting a noife fo loud, and even of pro-
ducing lightning and thunder, though it was impof-
fible for him to demonftrate the poffibility of it.
But, without detaining your attention on falfe ex-
planations which lead to nothing, I haften forward
to inform you, that it has been difcovered by incon-
testable proofs, that the phenomena of thunder are
always accompanied by the moft indubitable marks
of electricity.
Let a bar of metal, fay of iron, be placed on a
pillar of glafs, or any other fubftance whofe pores
are clofe, that when the bar acquires ele&ricity, it
may not efcape, or communicate itfelf to the body
which fupports the bar ; as foon as a thunder-ftorm
arifes, and the clouds which contain the thunder
come directly over the bar, you perceive in it a very
ftrohg electricity, generally far furpafling that which
art produces ; if you apply the hand to it, or any
other body with open pores, you fee burning from
it,
NATURE OF THUNDER. 135
it, not only a fpark, but a very bright flafh, with a
noife fimilar to thunder ; the man, who applies his
hand to it, receives a fhock fo violent that he is
ftunned. This furpaffes curiofity, and there is good
reafon why we mould be on our guard, and not ap-
proach the bar during a ftorm.
A profeffor at Peterfburgh, named Richmann, has
furnifhed a melancholy example. Having perceived
a refemblance fo ftriking between the phenomena of
thunder and thofe of electricity, this unfortunate na-
turalift, the more clearly to afcertain it by expert
ment, raifed, a bar of iron on the roof of his houfe,
cafed below in a tube of glafs, and fupported by a
mafs of pitch. To the bar he attached a wire, which
he conducted into his chamber, that as foon as the
bar mould become electric, the electricity might have
a free communication with the wire, and fo enable
him to prove the effects in his apartment. And it
may be proper to inform you, that this wire was
conducted in fuch a manner as no where to be in
contact but with bodies whofe pores are clofe, fuch
as glafs, pitch, or filk, to prevent the efcape of the
electricity.
Having made this arrangement, he expected a
thunder-ftorm, which, unhappily for him, foon came.
The thunder was heard at a diftance ; Mr. Rkhmann
was all attention to his wire, to fee if he could per-
ceive any mark of electricity. As the ftorm ap-
proached, he judged it prudent to employ fome pre-
caution, and not keep too near the wire ; but hap-
pening carelefsly to advance his cheft a little, he re-
K 4 ceivea
1^6 THE PHENOMENA OF
ceived a terrible ftroke, accompanied with a loud
clap, which ftretched him lifelefs on the floor.
About the fame time, the late Dr. Lieberkuhn and
Dr. Ludolf were about making fimilar experiments
in this city, and in that view had lixed bars of iron
on their ' houfes ; but being informed of the difafter
which had. befallen Mr. Richmann^ they had the bars
of iron immediately removed, and, in my opinion,
they acted wifely.
From this you will readily judge, that the air or
atmofphere muft become very electric during a
thunder-florin, or, that the ether contained in it muft
then be carried to a very high degree of comprefTion.
This ether, with which the air is furcharged, will
pafs into the bar, becaufe of it's open pores, and it
will become electric, as it would have been in the
common method, but in a much higher degree.
4/(6 Augujli 176L
LETTER XXXVII.
Explanation of the Phenomena of Lightning and
Thunder.
f J^HE experiments now mentioned inconteftably
JL demonftrate, therefore, that ftormy clouds' are
extremely electrical, and that, confequently, their
pores are either furcharged with ether, or exhaufted,
as both ftates are equally adapted to electricity. But
I have very powerful reafons for believing that this
electricity is pofitive, that the ether in them is com-
preifed
LIGHTNING AND THUNDER. 1 37
preffed to the higheft degree, and, confequently, fo
much the more elaftic than elfe where.
Such ftorms ufually fucceed very fultry weather.
The pores of the air, and of the vapours floating in
it, are then extremely enlarged, and filled with a
prodigious quantity of ether, which cafily takes pof-
feffion of all the empty fpaces of other fubftances.
Bat when the vapours collect in the fuperior regions
of our atmofphere, there to form clouds, they have
to encounter exceflive cold. Of this it is impoflible
to doubt, from the hail which is frequendy formed
in thefe regions ; this is a fuhicient proof of conge-
lation, as well as the mow which we find on the tops
of very high mountains, fuch as the Cordeliers,
while extreme heat prevails below.
Nothing then is more certain, or better eftablifhed
by proof, than the exceflive cold which umverfally
prevails in the upper regions of the atmofphere,
where clouds are formed. It is equally certain, that
cold contracts the pores of bodies, by reducing them
to a fmailer fize : now, as the pores of the vapours
have been extremely enlarged by the heat, as foon
as they are formed aloft into clouds, the pores con-
tract, and the ether which filled them, not being able
to eicape, becaufe thofe of the air are very clofe, it
needs muft remain there : it will be of courfe com-
preiTed to a much higher degree of denlity, and, con-
fequently, it's elafticity will be fo much the greater.
The real ftate of ftormy clouds, then, is this, the
ether contained in their pores, is much more elaftic
than ufual, or, in other words, the clouds have a po-
fitive
138 THE PHENOMENA OP
fitive electricity. As they are only an afTemblage o£
humid vapours, their pores are very open, but be-.
ing furrounded by the air whofe, pores are cjofe, this
ether could not efcape but very imperceptibly. But
if any perfon, or any body whatever, with open pores,
were to approach it, the fame phenomena which
electricity exhibits would prefent themfelves ; a very
vehement fpark, or rather a real flam, would burft
forth. Nay more, the body would uridergo a very
violent mock by the difcharge, from the impetuofity
with which the ether in the cloud would rum into
it's pores. This ihock might be indeed fo violent as
to deflroy the ftructure ; and, finally, the terrible
agitation of the ether which burfls from the cloud,
being not only light, but a real fire, it might be
capable of kindling and confuming combuftible bo-
dies.
Here, then, you will diftinguim all the circum-
ftances which accompany thunder ; and as to the
noife of thunder, the caufe is very obvious, for it is
impoilible the ether fhould be in fuch a Hate of agi-
tation, without the air itfelf receiving from it the
moft violent concuffions, which forcibly impel the
particles, and excite a dreadful noife. Thunder, then,
burfts forth, as often as the force of ether contained
in the clouds is capable of penetrating into a body,
where the ether is in it's natural ftate, and whofe
pores are open : it is not even neceffary that fuch
body mould immediately touch the cloud.
What I have faid refpecling the atmofphere of
electrified bodies, principally takes place in clouds ;
7 and
LIGHTNING AND, THUNDER. 1 39
and frequently, during a ftorm, we are made fenfible
of this electric atmofphere by a Hilling air, which is
particularly oppreffive to certain perfons. As foon
as the cloud begins to diffolve into rain, the air, be-
coming humid by it, is charged with an electricity
by which the commotion may be conveyed to bodies
at a very great diftance.
It is obferved that thunder ufually ftrikes very ele-
vated bodies, fuch as the fummits of church-fpires,
when they confift of fubftances with open pores, as
all metals are ; and the pointed form contributes not
a little to it. Thunder frequently falls, likewife, on
water, the pores of which are very open ; but bo-
dies with clofe pores, as glafs, pitch, fulphur, and
filk, are not greatly fufceptible of the thunder ftroke,
unlefs they are very much moiftened. It has been
accordingly obferved, that when thunder paffes
through a window, it does not perforate the glafs,
but always the lead or other fubftances which unite
the panes. It is almoft certain, that an apartment
of glafs cemented by pitch, or any other fubftance
with clofe pores,would be an effectual fecurity againft
the ravages of thunder.
§th Auguft, ij6l.
LETTER
I40 THE PHENOMENA OP
LETTER XXXVIII.
Continuation,
rT,HUNDER, then, is nothing elfe but the effect
•*- of the electricity with which the clouds are
endowed ; and as an electrified body, applied to an-
other in it's natural ftate, emits a fpark with fome
noife, and difcharges into it the fuperfluous ether,
with prodigious impetuofity ; the fame thing takes
place in a cloud that is electric, or furcharged with
ether, but with a force incomparably greater, becaufe
of the terrible mafs that is electrified, and in which,
according to every appearance, the ether is reduced
to a much higher degree of compreifion than we are
capable of carrying it by our machinery.
When, therefore, fiich a cloud approaches bodies,
prepared for the admiffion of it's ether, this difcharge
muft be made with incredible violence ; inftead o£ a
limple fpark, the air will be penetrated with a pro-
digious flafh, which, exciting a commotion in the
ether contained in the whole adjoining region of the
atrnofphere, produces a moll brilliant light ; and in
this lightning confiits.
n / The air is, at the fame time, put into a very vio-
lent motion of vibration, from which refults the
noife of thunder. This noife muft, no doubt, be ex-
cited at the fame inftant with the lightning ; but you
know that found always requires a certain quantity
of time, in order to it's tranfmiffion to any diftance,
and
LIGHTNING AND THUNDER. 141
and that its progrefs is only at the rate of about a
thoufand feet in a fecond ; whereas light, travels with
a velocity inconceivably greater. Hence we always
hear the thunder later than we fee the lightning :
and from the number of feconds intervening between
the flafh and the report, we are enabled to determine
the diitance of the place where it is generated, allow-
ing a thoufand feet to a fecond.
The body itfelf, into which the electricity of the
cloud is difcharged, receives from it a moft dreadful
ftroke ; fometimes it is fhivered to pieces ; fometimes
fet on fire and confumed, if combuftible ; fometimes
melted, if it be of metal : and, in fuch cafes, we fay
it is thunder-ftruck ; the effects of which, however
furprizing and extraordinary they may appear, are in
perfect confrftency with the well-known phenomena
of electricity.
A fword, it is known, has fometimes been by
thunder melted in the fcabbard, while the laft fuf-
tained no injury : this is to be accounted for, from
the opennefs of the pores of the metal, which the
-ether very eafily penetrates, and exercifes over it all
its powers, whereas the fubftance of the fcabbard is
more clofely allied to the nature of bodies with clofe
pores, which permit not to the ether fo free a tranf-
io'n.
It has likewife been found., that of feveral perfons,
on whom the thunder has fallen, fome only have
been ftruck by it ; and that thofe who were in the
middle fuSered no injury. The caufe of this pheno-*
menon likewife is manifefL In a group expofed to
\ a thunder
142 THE PHENOMENA OF
a thunder florin, they are in the greateft clanger who
Hand in the neareft vicinity to the air that is fur-
charged with ether ; as foon as the ether is difcharged
upon one, all the adjoining air is brought back to its
natural ftate, and confequcntly thofe who were neareft
to the unfortunate victim feel no effect ; while others,
at a greater diftance, where the air is ftill fufflcientry
furcharged with ether, are flruck with the fame
thunder clap.
In a word, all the ftrange circumftane'es, fo fre-
quently related, of the effects of thunder, contain
nothing which may not be eafiiy reconciled with the
nature of electricity.
Some philofophers have maintained, that thunder .
did not come from the clouds, but from the earth,
or bodies. However extravagant this fentiment may
appear, it is not fo abfurd, as it is difficult to diftin-
guifh, in the phenomena of electricity, whether the
fpark iffues from the body which is electrified, or
from that which is not fo, as it equally fills the fpace
between the two bodies ; and if the electricity is ne-
gative, the ether and the fpark are in effect emitted
from the natural or non-electrified body. But we
are fumciently affured that, in thunder, the clouds
have a pofitive electricity, and that the lightning is
emitted from the clouds.
You will be juftifiable' however in afking, if by
every ftroke of thunder, fome terreftriaj body is af-
fected ? We fee, in fact, that it very rarely ftrikes
buildings, or the human body ; but we know, at the
fame time, that trees are frequently affected by it, and
• that
LIGHTNING AND THUNDER. I43
that many thunder-ilrokes are difcliarged into the
earth and into the water. I believe, however, it
might be maintained, that a great many do not de-
fcend fo low, and that the electricity of the clouds is
very frequently difcliarged into the air or atmofphere.
The fmall opening of the pores of the air no longer
oppofes any obftruction to it, when vapours or rain
have rendered it fufhcientiy humid ; for then, we
know, the pores open.
It may very pofhbly happen, in this cafe, that the
fuperfluous ether of the clouds mould be difcharged
fimply into the air ; and when this takes place, the
ftrokes are neither fo violent, nor accompanied with
fo great a noife, as when the thunder burfts on the
earth, when a much greater extent of atmofphere is
put in agitation.
litb Augujly 1761.
LETTER XXXIX.
The Poffibility of preventing, and of averting, the Effecls
of Thunder.
|"T has been afked, Whether it might not be pof-
•*- fible to prevent, or to avert, the fatal effe&s of
thunder ? You are well aware of the importance of
the que (Hon, and under what obligation I mould lay
a multitude of worthy people, were I able to indicate
an infallible method of finding protection againfl
thunder.
The knowledge q,f the nature and effects of elec-
tricity,
244 0F PREVENTING AND AVERTING
tricity, permits me not to doubt that the thing is
poflible. I correfponded fome time ago with a Mo-
ravian prieft, named Procophis Divifch, who affured
me that_ he had averted, during a whole fummer,
every thunder-ftorm which threatened his own habi-
tation, and the neighbourhood, by means of a ma-
chine conftructed on the principles of electricity. Se-
veral perfons, fince' arrived from that country, have
allured me that the fact, is undoubted, and confirmed
by irrefiftible proof.
But there are many refpectable characters, who,
on the fuppofition that the thing is practicable, would
have their fcruples reflecting the lawfulnefs of em-
ploying fuch a prefervative. The ancient pagans, no
doubt, would have confidered him as impious, who
mould have prefurned to interfere with Jupiter, in
the direction of his thunder. Chriftians, who are
allured that thunder is the work of God, and that;
Divine Providence frequently employs it to punifh
the wickednefs of men, might with equal reafon allege,
that it were impiety to attempt to oppofe the courfe
of fovereign juftice.
Without involving myfelf in this delicate difcuf-
iion, I remark that conflagrations, deluges, and many
other general calamities, are likewife the means em-
ployed by Providence to puniih the fins of men ; but
no one, furely, ever will pretend, that it is unlawful
to prevent, or refift, the progrefs of a fire or an inun-
dation. Hence I infer, that it is perfectly lawful
to ufe the means of prevention againft the effects of
thunder, if they are attainable.
The
THE EFFECTS OF THUNDER. I45
The melancholy accident which befel Mr. Richmann
at Petersburg, demonftrates, that the thunder-ftroke
which this gentleman unhappily attracted to himfelf,
Would undoubtedly have fallen fome where elfe, and
that fuch place thereby efcaped ; it can therefore no
longer remain a queflion whether it be pofiible to
conduct thunder to one place in preference to ano-
ther 5 and this feems to bring us near our mark.
It would, no doubt, be a matter ofltill greater im-
portance, to have it in our power to diveft the clouds
of their electric force, without being under the ne-
ceflity of expofing any one place to the ravages of
thunder ; we fhould, in that cafe, altogether prevent
thefe dreadful effects, which terrify fo great a part of
mankind.
This appears by no means impoffible ; and the
Moravian prieft, whom I mentioned above, unquef-
tionably effected it j for I have been affured, that his
machinery fenfibly attracted the clouds, and con-
ftrained them to defcend quietly in a diftiilation,
without any but a very diftant thunder-clap.
The experiment of a bar of iron, in a very elevated
fituation, which becomes electric on the approach of
a thunder-ftorm, may lead us to the conftruction of
a fimilar machine, as it is certain, that in proportion
as the bar difcharges its electricity, the clouds mull
lofe precifely the fame quantity ; but it muft be con-
trived in fuch a manner, that the bars may' -immedi-
ately discharge the ether which they have attracted.
It would be neceffary, for this purpofe, to procure
for them a free communication with a pool, or with
Vol. II. L the
I46 OF PREVENTING AND AVERTING
the bowels of the earth, which, by means of theif
open pores, may eafily receive a much greater quan-
tity of ethers and difperfe it over the whole immenfe ,
extent of the earthj fo that the comprefiion of the
ether may not become fenfible in any particular fpot.
This communication is very eafy by means of chains
of iron, or any other metal, which will, with great
rapidity, carry off the ether with which the bars are
furcharged.
I would advife the fixing of ftrong bars of iron, in
very elevated fituations, and feveral of them together,
their higher extremity to terminate in a point, as
this figure, is very much adapted to the attraction of
electricity. I would, afterwards, attach long chains
of iron to thefe bars, which I would conduct, under
ground into a pool, lake, or river, there to difcharge
the electricity ; and I have no doubt, that after mak-
ing repeated efiays, the means may be certainly dis-
covered of rendering fuch machinery more commo-
dious, and more certain in its effect.
It is abundantly evident, that on the approach of
a thunder-ftorm, the ether, with which the clouds are
furcharged, would be tranfmitted in great abundance
into thefe bars, which would thereby become very
electric, unlefs the chains furnifhed to the ether a free
pafiage, to fpend itfelf in the water, and in the bowels
of the earth.
The ether of the clouds would continue, therefore,
to enter quietly into the bars, and would, by its agi-
tation, produce a light, which might be viiible on the
pointed extremities.
Such
THE EFFECTS OF THUNDER. I47
Such light is, accordingly, often obferved, during
a ftorm, on the fummit of fpires, an infallible proof
that the ether of the cloud is there quietly difcharging
itfelf ; and every one confiders this as a very good
fign, of the harmlefs abforption of many thunder-
ftrokes.
Lights are likewife frequently obferved at fea, on
the tops of the m aft s of fhips, known to failors by the
name of Caftor and Pollux ; and when fuch figns are
viable, they confider themfelves as fafe from the
ftroke of thunder.
Moft philofophers have ranked thefe phenomena
among vulgar fuperftitions ; but we are now fully
allured, that fuch fentiments are not without foun-
dation ; indeed they are infinitely better founded
than many of our philofophic reveries.*
l$tb Jnguft, 1 76 1.
* It was deemed improper to divert the reader's attention from
Euler,s train of thought, on the fubjedt of electricity, by notes on
particular paffages, according as the obfervations occurred. But
now that the fubject is clofed, I am happy to infert, at once, a few
general remarks on Eulcr's theory y fu mimed by a gentleman well-
known in the world of fcience, both by his literary productions,
and by his various and highly improved mathematical inftruments;
and who has lately enriched it by his valuable Lectures on Natural
and Experimental Philofophy, in 5 vols. 8vo. I mean Mr. George
Adams, of Fleet-ftreet. — E. E.
" However Mr. Euhr may have deviated from the prefent
theories of electricity, in the explanation of particular phenomena,
the great outline of his fyftem feems to be confirmed by the con-
jectures of Ne-zvto;-:, the opinions of W~atfon, Franklin, Wilforn, Eeles,
&c." Thefe great men concur in fuppohng an etherial fluid to be
univerfaliy diffeminated through all matter ; and every experiment
L^ proves,
148' OF PREVENTING AND AVERTING
Proves, that its active properties depend on a folution of continuity
(which is nearly related to a change in the pores of bodies) whether
produced by local motion, rupture of parts, friction, expanfion by
heat, or condenfation by cold. Still there is no real ground for
fuppofing that thofe (kites of electricity, called pofitive and negativer.
depend on the pores of bodies being more or lefs open, for it is-
highly probable, that the two ftates are always produced, at the
feme time, in all bodies, and either ftate may be exhibited by the
fame body, under certain circumftances, which can have no effect
on the pores of the bodies concerned.
It is clear, that all electric appearances depend on an invilible
fluid, of whofe effects, while it remains in its natural ftate, we are
totally ignorant; but, whenever this ftate is diflurbed, thofe ap-
pearances which we call electrical take place. Of thefe I mail'
notice a few, fomewhat more fully than has been done by Mr.
Euler. Obferving, firft, that fince his time the catalogue of thofe
fubftances which tranfmlt, with eafe, the electric fluid, as well as
thofe that do not conduct it, has been confiderably increafed ; and
none have yet been found but what have more or lefs affinity with
the electric fluid. It is worthy of remark, that many bodies which
are non-conductors when cold, will tranfmit the fluid, when they
are heated ; a circumftance which feems to confirm the ideas of
Mr. Euler.
Though Mr. Euler has endeavoured to explain the mechanifm of
electric attraction, and repulfion, he hasnot pointed out the general
laws by which it is governed. Thefe are, Firft, that bodies elec-
trified pofitively repel each other : Secondly, that bodies electrified
negatively repel each other : Thirdly, bodies electrified by contrary
powers ftrongly attract each other : Fourthly, bodies that are elec°-
trifled attract thofe fubftances which, are not electrified.
No experiments, on this fubject, have engaged the attention of
philofophers more than thofe on the Leyden phial. The myfteries
of this experiment are far from being unveiled, and we are in pof-
feffion of no theory that will clearly account for it. Dr. Franklin
fhewed, that the Leyden phial could not be charged, unlefs fome
conducting fubftance, in contact with the outfide, was alfo con-,
rfected with the ground, &.c. He. maintained,, that the furplus-
electricits^
THE EFFECTS OF THUNDER. 1 49
tilectricity which was received, by one of the coated furfaces of the
phial, was actually taken from the other; that one fide was al-
ways positively, the other always negatively, electrified. This
theory has been fhewn to be defective, and it has-been proved that,
while the phial is charging, both fides are electrified pofitively.
By connecting feveral bottles together, the electric power may
be increafed almoft at pleafure, animals may be be killed, and po-
larity may be given to magnetic needles.
It has been already obferved, that the electric fluid, in patting
from one body to another, emitted rays of light ; later experiments
have fhewn that there is fcarce any fubftanee, folid or fluid, but
what may be rendered luminous by paffing through it the electric
fluid. It has alfo been found, in many inftances, to produce the
fame effects as culinary fire ; thus it will raife the thermometer,
accelerate vegetation, and promote evaporation, &c.
After that aftonifhing difcovery, by which the fimilarity of
Lightning and Electricity was proved, conducting rods were adaped
to buildings, to preferve them from being injured by lightning.
Thefe are, in general, allowed to be ufeful, though not fo exten-
fively as was at firft imagined ; and, though they may conduct the
lightning that falls upon, or meets with, them, fafely to the ground,
yet it is abfurd to fuppofe, that a conductor can prevent the light-
ning from flriking a building, or is capable of exhaufting the at-
mofphere of its electricity.
One of the moft brilliant difcoveries, concerning Electricity, is
that of its activity in carrying on the functions of animal life.
Mr. Waljh has fhewn, that the powers of the Torpedo, and the
Gymnotus Electricus, like thofe of the Leyden phial, might be
extended to any diftance through a medium of conducting fub-
ftances, and that thofe bodies which impede the discharge of an
eledlrical accumulation, had the fame influence on the powers of
the Torpedo, &c. Through a fmall interval, in the circuit formed
to conduct the influence of thefe animals, a fpark of light has been
made to appear, which has fully eitablifhed the fimilitude between
the electrical fluid of thefe animals and that of nature at large.
Many inftances might be introduced to fhew its agency in the
human frame, but none can be offered of more importance to
L 3 * mankind,
I50 ■ ON THE LONGITUDE.
mankind, than thofe which prove its efficacy as a medicine : it
has been applied with fuccefs, to relieve the fufferings of man-
kind, and, at a great hofpital in this metropolis, under the cau-
tious eye of public icvutiny, has obtained ah eftabliflied rank in
the art of healing.
LETTER XL.
On the celebrated Problem of the Longitude : general
Defcripiion of the Earthy of its Axis,, its two Poles,
and the Equator.
YOU will by this time, no doubt, imagine that
enough has been faid of electricity ; and indeed
I have nothing farther to add on that fubject ; and
am, of courfe, not a little embarraffed about the
choice of one worthy of your attention.
In order to determine my choice, I think myfelf
obliged to take into consideration thofe fubjects
which moft materially intereft human knowledge,
and which Authors of celebrity moft frequently
bring forward. Thefe are Subjects, refpecting which,
it is to be prefumed, perfons of quality have conii-
derable information.
As you mult, unquestionably, have heard frequent
mention made of the celebrated problem of the lon-
gitude, to the folution of which the Britifh nation
has propofed a moft magnificent premium, I prefume
that my labour will not be wholly thrown away, if
I employ it in laying before you a fair State of that
important quefdon. It has fuch an intimate con-
nection with the knowledge of our terraqueous globe,
that
ON THE LONGITUDE.
*5f
ignorant of it, It will
accordingly furnifh me with an opportunity of ex-
plaining a variety of interefting articles, which, I
flatter myfelf, you would with to fee elucidated.
I begin then with a general defcription of the
earth, which may be confidered as a globe, though
it has been difcovered by recent obfervation, that its
real figure is a fpheroid, fomewhat flattened ; but
the difference is fo fmall, that it may, for the prefent,
be altogether neglected.
The firft thins; to be remarked on the cdobe of the
earth, are two points on it's furface, denominated
the two poles of the earth. Round thefe two points
the globe of the earth every day revolves, as you
turn a ball fixed between the two points of a turn.
ing machine. This motion is called the daily or di-
urnal motion of the earth, each revolution of which
is performed in about twenty-four hours. Or, to
fpeak according to appearances, you know that the
whole heavens, which we confider as a concave ball,
within wrhofe circumference the earth revolves, ap-
pear to turn round the earth in the fame fpace of
twenty-four hours. This motion is likewife per-
formed round two fixed points in the heavens, de-
nominated the poles of heaven ; now if we conceive
a ftraight line drawn from one of thefe poles of hea-
ven to the other, that line will pafs through the
centre of the earth.
But you will eafily comprehend, that the appear-
ance muft be the fame, whether the earth turns
round thefe poles, while the heavens remain in a
L 4 ftate
I52 ON THE LONGITUDE.
ftate of reft ; or whether the heavens revolve round
their poles, the earth remaining at reft. On either
fuppolitiou we are equally led to the knowledge of
the poles of the earth, the foundation not only of
aftronomy, but likewife of geography.
Lety%. 1. of plate I. reprefent the ~ globe of the
earth, whofe poles are the points A and B ; one of
thefe poles, A, is named the Jouth or antarclic pole,
the other, B, is denominated the north or arclic pole.
This laft is nearer to the region of the globe which
we inhabit.
I remark, that thefe two poles are directly oppo-
fite to each other ; in other words, were a ftraight
line AB to be drawn directly through the earth, it
would pafs precifely through the middle C, that is
to fay, through the centre of the earth. This ftraight
line AB has accordingly it's appropriate name, and
is called the axis of the earth, which being produced
in both directions to the heavens, will terminate in
the two points which are called the poles of heaven ;
and to which we give the fame names as to thofe of
the earth.
Thefe two poles of the earth are by no means a
mere fiction, or a fpeculation of aftronomers and
geographers ; but are really moft efTential points
marked on the furface of our globe ; for it is well
known, that the nearer we approach thefe two
points, the colder and more rugged the face of na-
ture becomes, to fuch a degree that the regions ad-
jacent to the poles are abfolutely uninhabitable, from
the exceffive cold which prevails there during the
winter.
ON THE LONGITUDE. 1 53
winter. No one inftance, accordingly, has been pro-
duced of any traveller, whether by land or water,
who has reached either of the poles. It may be af-
firmed, therefore, that thefe two fpots of the earth
are altogether inaccefiible.
Having thus determined the two poles of the earth
A and B, we may conceive the whole globe divided
into two hemifpheres, DBE and DAE, each of
which terminates in one of the poles as its fummit.
For this purpofe we are to fuppofe the globe bifected
through its centre C, fo that the fection fhall be per-
pendicular to the axis of the earth ; this fection will
mark, on the furface, a circle encompafling the whole
globe, every where equally diftant from the two
poles. This furrounding circle is denominated the
equator. The regions adjacent to it are the hotteft,
and on that account, as the ancients believed, almoft
uninhabitable ; but they are now found to be ex-
ceedingly populous, though the heat be there almoft
infupportable.
But as you remove from the equator, on either
fide, toward the poles, the countries become more
and more temperate, till, at laft, on approaching
too near the poles, the cold becomes intolerable.
As the equator divides the earth into two hemi-
fpheres, each bears the name of the pole contained
in it ; thus the half DBE, which contains the north
pole, is denominated the northern hcmifphere, and in
it is fituated all Europe, almoft the whole of Alia,
part of Africa, and the half of America. The other
hemifphere is, from it's pole, denominated the /out hern
hemi/pJj
154 MAGNITUDE OP THE EARTH.
hemifphere, and contains the greateft part of Africa,
the other half of America, and feveral ifles, which
geographers attribute to Afia, as you will recollect
to have feen in maps of the world.
1 2t/j Auguftt 1 76 1 .
LETTER XLI.
Of the Magnitude of the Earth ; of Meridians, and the
Jhotteft Road from Place to Place.
"AVING diftincHy fixed the idea of the poles
of the earth and of the equator, which you
can much more eafily imagine on a globe, than I
can reprefent by a figure, every other neceffary idea
will readily follow from thefe.
I mull, however, fubjoin a further elucidation of
confiderable importance. The axis of the earth
palling from one pole to the other, through the cen-
tre of the earth, is a diameter of the globe, and
confequently is double the length of the radius. A
radius of the earth, or the diftance from every point
on the furface to the centre is computed to be 860
German miles ;* the axis of the earth will therefore
contain 1720 German miles. And the equator be-
ing a circle whofe centre is like wife that of the earth,
it will have the fame radius, namely 860 miles, the
* About 3956 miles Englifh, or 1432 French leagues ; the axis
of the earth will accordingly be 7912 miles Englifh, or 2864
French leagues; and the circumference at the equator 235736
miles Englifh, about 8600 leagues of France. — E.E.
diameter
MAGNITUDE OF THE EARTH. 1$$
diameter of the equator will accordingly be 1720
miles, and it's whole circumference 5400 miles nearly;
fo that if you were to make a tour of the globe, fol-
lowing the tract of the equator, you muft perform
a journey o^ almoft 5400 German miles. This will
give you fome idea of the magnitude of the earth.
The equator being a circle, it is fuppofed to be
divided into 360 equal parts, named degrees : a de-
gree of the equator contains therefore 15 German
miles,* as 15 times 360 make 5400.
Every degree is again fubdivided into 60 equal
parts, called minutes, fo that every minute contains
the fourth part of a German mile, or about 6000
feet ; a fecond being the iixtieth part of a minute,
will contain 100 feet.
It being impoffible to reprefent a globe, on paper,
any other way than by a circle, you mud fuppiy this
defect by imagination. Accordingly AB, (plate I.
jig. 1.) being the two poles of the earth ; B, the
north, and A, the fouth ; DMNE will reprefent the
equator, or rather that half of it which is turned
toward us, the other being concealed oh the oppofite
fide.
The line DMNE reprefents then a femi-circle, as
well as BD A and BE A; all thefe femi-circles having
their centres at that of the globe, C. It is poffible
to imagine an infinite number of other femi-circles,
all of them drawn through the two poles of the
earth A and B, and pailing through every point of
* 69 Englifti.
the
l$6 MAGNITUDE OF THE 5ARTH.
the equator, as BMA, BN A : thefe will all be fimi-
lar to the firft BDA and BE A; though in the fi-
gure their form appears very different. Imagination
mult correct; this, and the fact is apparent on a real
globe.
All thefe femi-circles drawn from one pole to the
other, through whatever point of the equator they
may pafs, are denominated meridians: or rather, a
meridian is nothing elfe but a femi-circle which, on
the furface of the earth, is drawn from one pole to
the other ; and you can eafily comprehend, that,
taking any place whatever on the furface of the
earth, fay the point L, you can always conceive a
meridian BLMA, which, palling through the two
poles, takes in it's way the point L. This meridian
then is named the meridian of L. Suppofing, for
example, L to be Berlin, the femi-circle BLMA
would be the meridian of Berlin ; and in like man-
ner refpecting every other fpot of the earth.
You can reprefent to yourfelf a globe, on the
furface of which are defcribed all the countries of
the earth, the continent, as well as the fea with it's
iflands. This artificial globe, denominated the ter~
rcfirial or terraqueous globe, you muft no doubt be
acquainted with. As to all meridians, which can
poflibly be drawn upon it, and a great number of
which actually are traced, I remark, that each, being
a femi-circle, is divided by the equator into two
equal parts, each of which is the fourth part of a
circle, that is an arch of 90 degrees. Accordingly,
' BD, BM, BN, BE, are fourth parts of a circle as
well
MAGNITUDE OF THE EARTH. 1 57
wdl as AD, AM, AN, AE; each therefore contains
90 degrees : and it may be farther added, that each
is perpendicular to the equator, or forms right angles
with it.
Again, were a perfon to travel from the point of
the equator M, to the pole B, the ihorteft road
would be to purfue the track of the meridian MLB,
which being an arch of 90 degrees, and a degree
containing 15 German miles, would contain 1350
miles,* the diftance to be paffed in going from the
equator to either of the poles.
You will recollect, that the ihorteft road from
place to place, is the ftraight line drawn through
any two places ; here the ftraight line, drawn from
the point M, in the equator, to the pole B, would
fall within the earth, a route which it is impofiible
to purfue, for we arc fo attached to the furface of
the earth, that we cannot remove from it. For this
reafon the queftion becomes exceedingly different.,
when it is afked, What is the ihorteft road, leading
from one fpot on the furface of a globe to another ?
This ihorteft road is no longer a ftraight line, but
the fegment of a circle, defcribed from one point of
the furface to another, and whofe centre is precifely
that of the globe itfelf. This is accordingly in per-
feci; harmony with the cafe in queftion ; for to travel
from the point M in the equator, to the pole B, the
arch of the meridian MLB, which I have reprefented
as the ihorteft road, is in effect a fegment of the circle
whofe centre is precifely that of the earth.
* A-bout6200 miles Englifh, or 2250 French leagues.
I58 MAGNITUDE OF THE EARTH.
In like manner, if we confider the fpot L, fituated
in the meridian BLMA, the fhorteft road to go
thence to the pole B, will be the arch LB; and if
we know the number of degrees which this arch
contains, allowing 1 5 German miles to a degree, we
fhall have the length of the road. But if you were
difpofed to travel from the fame fpot to the equator,
by the fhorteft track, it would be neceffary to purfue
the track of the arch of the meridian LM, the num-
ber of degrees contained in which, reckoning 1 5 Ger-
man miles to a degree, would give the diftance.
We mull be fatisned with exprefling thefe diftances
in degrees, it being fo eafy to reduce them to Ger-
man miles, while other nations employ miles of va-
rious length, fome greater, fome fmaller. Taking,
then, the city of Berlin for the fpot L, we find that
the arch LM, which leads to the equator, contains 52
degrees and a half; confequently to travel from Ber-
lin to the equator, the fhorteft road is 787 German
miles and a half. But if any one were to go from
Berlin to the north pole, he muft follow the direction
of the arch BL, which containing 37 degrees and a
half, would be 562 German miles and a half. Thefe
two diftances added, give 1350 German miles for the
extent of the arch BLM, which is the fourth part
of a circle, or no degrees, which contain, as we have
feen, 1350 German miles.
22'/ Augufi, 1 76 1.
LETTER
OF LATITUDE. 1 59
LETTER XLII.
Of Latitude, and its Influence on the Seafons, and the
Length of the Day.
I BE GIN once more with the fame figure, (plate L
fig. 3.) which mult by this time be abundantly-
familiar to you. The whole circle reprefents the
globe of the earth ; the points A and B it's two
poles ; B the north or arctic, and A the fouth or
antarctic ; fo that the ftraight line B A drawn within
the earth, and palling through it's centre C, is the
axis of it. Again DME is the equator which di-
vides it into two hemifpheres, DBE the northern,
and DAE the fouthern.
Let us now take any fpot whatever, fay L, and
draw it's meridian BLMA, which, being a femi-
circle, paffes through the point L, and the two poles
B and A. This then is the meridian of the place L,
divided by the equator at M into two equal parts,
making two-fourths of a circle, each of which con-
tains 90 degrees. I remark farther, that the arch
LM, of this meridian, gives us the diftance of the
place L from the equator, and that the arch LB ex-
preffes the diftance of the fame place L, from the
pole B.
This being laid down, it is of importance to ob-
ferve that the arch LM, or the diftance of L from
the equator, is denominated the latitude of the place L ;
fo that the latitude of any place on the globe, is no-
thing
l6o OF LATITUDE*
thing elfe but the arch of the meridian of that place,
which is intercepted between the equator and the
given place : in other words, the latitude of a place,
is the diflance of that place from the equator, ex-
prefling fuch diilance by degrees, the quantity of
which we perfectly know, as each degree contains
15 German miles.
You will readily comprehend, that this diftance
muft be diftinguifhed, according as the given place
is in the northern, or fouthern hemifphere. In the
former cafe, that is, if the given place . is in the
northern hemifphere, we fay it has north latitude %
but if it is in the fouthern hemifphere, we fay it is
m fouth latitude.
Taking Berlin as an inftance, we fay it is in 52
degrees and 3 r minutes of north latitude ; the lati-
tude of Magdeburg is, in like manner, northern, 52
degrees and 1 9 minutes. But the latitude of Batavia
in the Eaft Indies is 6 degrees 15 minutes fouth;
and that of the Cape of Good Hope in Africa, is
likewife fouth 34 degrees 15 minutes.
I remark by the way, that for the fake of abbre-
viation, inftead of the word degree we affix a fmall
cipher (°) to the numeral characters, and inftead of
the word minute a fmall flanting bat ('), and inftead
of fecond two of thefe (") j thus the latitude of the
obfervatory at Paris is 48° 50'' 10", N. that is 48
degrees, 50 minutes and 10 feconds North. In Peru
there is a place named Vlo, whofe latitude has been
found to be 170 36' 15", S. that is, 17 degrees, 36
minutes and 1 5 feconds South. Hence you will un-
, 2 derftand,
OF LATITUDE. iGl
derftand, that if a place were mentioned whofe lati-
tude was o° o' o/;j fiich place would be precifely un-
der the equator, as its diftance from the equator is o,
or nothing ; and in this cafe it is unncceffary to affix
the letter N or S. But were it poffible to reach a
place whofe latitude was 900 N. it would be precifely
the north pole of the earth, which is diftant from the
equator the fourth of a circle or 90 degrees. This
will give you a clear idea of what is meant by the
latitude of a place, and why it is expreffed by de-
grees, minutes, and feconds.
It is highly important to know the latitude of
every place;, not only as effehtial to Geography, in
the view of affigning to each its exact fituation on.
geographical charts, but likewife becaufe on the la-
titude depend the feafons of the year, the inequali-
ties of day and night, and confequently the tempe-
rature of the place.- As to places fituated directly
under the equator, there is fcarcely any perceptible
variation of the feafons, and through the whole year
the days and nights are of the fame length, namely
1 2 hours. For this reafon the equator is likewife
denominated the equinoctial line : but in proportion
as you remove from the equator, the more remark-
able is the difference in the feafons of the year, and
the more likewife the days exceed the nights in fum-
mer, whereas, reciprocally, the days in winter are as
much fhorter than the nights.
You know that the longeft days, in thefe northern
latitudes, are toward the commencement of our
fummer, about the 21ft of June j the nights, of con-
. Vol. II. M iequence,
l62 • OF LATITUDE.
iequence, are then the fliorteft; and that toward the
beginning of our winter, about the 23d of Decem-
ber, the days are fliorteft and the nights longeft : fo
that every where, the longeft day is equal to the
longeft night. Now in every place, the duration of
the longeft day depends on the latitude of the place.
Here, at Berlin, the longeft day is 16 hours and 38
minutes, and confequently the ihorteft day in winter
is 7 hours 22 minutes. In places nearer the equator,
or whofe latitude is lefs than that of Berlin, which is
5 20 32', the longeft day in fummer is lefs than 16
hours 38 minutes, and in winter the fliorteft day is
more than 7 hours 22 minutes. The contrary of
this takes place on removing farther from the equa-
tor : at Petersburg, for example, whofe latitude is
60 degrees, the longeft day is 18 hours 30 minutes,
and confequently the night is then only 5 hours 30
minutes : in winter, on the contrary, the longeft
night is 18 hours 30 minutes, and then the day is
only 5 hours 30 minutes. Were you to remove ftiil
farther from the equator, till you came to a place
whofe latitude was 66° 30', the longeft day there
would be exactly 24 hours,, in other words, the fun
would not fet at that place, at that feafon ; whereas
in winter the contrary takes place, the fun not rifmg
at all on the 23d of December, that is, the night
then lafting 24 hours. Now at places ftill more re-
mote from the equator, and confequently nearer the
pole, for example, at Warthuys in Swedifti Lapland,
this longeft day lafts for the fpace of feveral days to-
gether, during which the fun abfolutely never fets ;
and
OF PARALLELS. 1 6$
and the longeft night, when the fun never rifcs at
all, is of the fame duration.
Were it poffible to reach the pole itfelf, we mould
have day for fix months together, and, during the
other fix, perpetual night. . From this you compre-
hend of what importance it is to know accurately
the latitude of every fpot of the globe.
22</ Auguji, 1 761.
LETTER XLIII.
Of Parallels, of the firjl Meridian, and of Longitude.
HAVING informed you, that in order to find
the meridian of any given place, fay L, it is ne-
ceffary to draw on the furface of the earth a femi-
circle B L M A, pafTmg through the two poles B and
A, and through the given place L ; I remark, (plate
J. fig. 4. J that there is an infinite number of other
places, through which this fame meridian paffes,
and which are confequently all faid to be iituated
under the fame meridian, whether in the northern
hemifphere, between B and M, or in the fouthern,
between M and A.
Now all the places, Iituated under the fame meri-
dian, differ as to latitude, fome being nearer to, or
more remote from, the equator than others. Thus
the meridian of Berlin paffes through the city of
Meiffe, and nearly through the port of Triefte, as
well as many other places of lefs note.
You will likewife pleafe to obferve that a great
many places may have the fame latitude, that is, may
M 2 be
I 6*4 OF PARALLELS.
be equally diftant from the equator, but all of them
lltuated under different meridians. In fact, if L is
the city of Berlin, whofe latitude, or the arch LM
contains 520 31', it is poffible under any other meri-
dian B N A, a place I, the latitude of which, or the
arch 1 N, &ail like-wife be 5 20 3 1' j fuch are the points
F and G, taken in the meridians BD A, BEA. And
as a meridian may be drawn through every point of
the equator, in which there fhall be a place whofe
latitude is the fame with that of Berlin, or the place
L, we fhall have an infinite number of places, all of
the fame latitude. They will be all fituated in the
circle FL I G, all the points of which being equally
diftant from the equator, it is denominated a. parallel
circle to the equator, or limply a parallel. A parallel
on the globe, then, is nothing elfe but a circle parallel
to the equator, that is, all the points of which are
equidiftant from it ; hence it is evident, that all the
points of a parallel are likewife equidiftant from the
poles of the earth.
As it is poflible to draw fuch a parallel through
every place on the globe, we can conceive an infinite
number-of them, all differing in refpect of latitude,
each having a latitude, whether north or fouth, pe-
culiar to itfelf.
You muft likewife be abundantly fenfible, that the
greater the latitude is, or the nearer you approach to
either of the poles, the fmaller the parallels become,
till at laft, on coming to the very poles, where the
latitude is 900, the parallel is reduced to a fingle point.
But, on the contrary, as you approach the equator,
or
OF PARALLELS. lC>$
or the fmallcr the latitude is, the greater are the pa-
rallels ; till at laft, when the latitude becomes o, or
nothing, the parallel is loft in the equator. It is ac-
cordingly by the latitude that we diftjnguifh them ;
thus the parallel of 300, is that which partes through
every place whofe latitude is 30 degrees, but it is
neceffary to explain yourfelf, according as you mean
north or fouth latitude.
On confulting an accurate map, you will obferve
that Hanover is fituated under the fame parallel with
Berlin, the latitude of both being 520 31', and that
the cities of Brunfwick and Amfterdam fall nearly
under the fame parallel ; but that the meridians pair-
ing through thefe places are different. If you know
the meridian and the parallel under which any place
is fituated, you are enabled to afcertain its actual po-
sition on the globe. If it were affirmed, for example,
that a certain place is fituated under the meridian
BNA, and the parallel FLG, you would only have
to look where the meridian BNA is interfered by
the parallel FLG, and the point of interfeclion I, will
give the true pofition of the given place.
Such are the means employed by geographers to
determine the real fituation of every place on the face
of the globe. You have only to afcertain its parallel,
or the latitude, and its correfponding meridian. As
to the parallel, it is eafy to mark and diftinguifh it
from every other j you have only to indicate the la-
titude, or diftance from the equator, according as it
is north or fouth : but how dcfcribe a meridian, and
iguifh it from every other ? They have a per-
M3 feet
1 66 OF PARALLELS.
feet refemblance, they are all equal to each other, and
no one has a fpecial and diftinctive mark. It depends
therefore upon ourfelves to make choice of a certain
meridian, and to fix it, in order to refer all others to
that one. If, for example, in the figure referred to
at the beginning, we were to fix on the meridian
BDA, it would be eafy to indicate every other me-
ridian, fay BMA, by fimply afcertaining on the
equator the arch DM, contained between the fixed
meridian BDA and the one in queflion BMA, ad-
ding only in what direction you proceed from the
fixed meridian toward the other, whether from eaft
to weft, or weft to eaft.
This fixed meridian, to which every other is re-
ferred, is called xhtjirji meridian ; and the choice of
this meridian being arbitrary, you will not think it
ftrange that different nations fhould have made a
different choice. The French have fixed on the ifle
of Ferro, one of the Canaries, for this purpofe, and
draw their firft meridian through it. The Germans
and Dutch draw theirs through another of the Canary
iflands, called Teneriffe. But whether you follow the
French or German geographers, it is always neceffary
carefully to mark on the equator the point through
which the firft meridian paffes; from this point you
afterwards reckon by degrees, the points through
which all other meridians pafs ; and both French and
Germans have agreed to reckon from weft to eaft.
If, therefore, in the figure to which I have already
referred, the femicircle BDA be the firft meridian
and the points of the equator M and N were fituated
toward
FIRST MERIDIAN. 1 6/
toward the eaft, you have only, in order to mark any
other meridian, fay BMA, to indicate the magnitude
of the arch DM ; and this arch is what we call the
longitude of all the places fituated under the meridian
BMA. In like manner, all the places fituated under
the meridian BNA have their lonsritude determined
o
by the arch of the equator DN, expreffed in degrees,
minutes and feconds.
tyb Augujl, 1 761.
LETTER XLIV.
Choice of the Firfi Meridian.
YOU have now received complete information
refpecting what is denominated the latitude and
the longitude of a place on the furface of the globe.
Latitude is computed on the meridian of the given
place, up to the equator ; in other words, it is the
diftance of the parallel paffing through that place,
from the equator ; and to prevent all ambiguity, it
is neceffary to exprefs whether this latitude or diftance
•is north or fouth.
As to longitude, we muft determine the diftance
of the meridian of the given place from the firft me-
ridian ; and this diftance is computed on the equator,
from the firft meridian to the meridian of the given
place, always proceeding from weft to eaft ; in other
words, longitude is the diftance of the meridian of
the given place, from the firft, computing the degrees
on the equator, as I have juft now faid.
M 4 Wt
l68 „ FIRST MERIDIAN.
We always compute, then, from the firft meridian
eaftward ; and it is evident that when we have com-
puted up to 360 degrees, we are brought back pre-
cisely to the firft meridian, as 360 degrees * complete
the circumference of the equatqr. Accordingly,
were any particular place found to be in the 359th
degree of longitude, the meridian of that place would
be only one degree diftant from the firft meridian,
but toward the weft. In like manner, 3500 of lon-
gitude would exactly correfpond with a diftance of
io°weftward. For this reafon, in order to avoid
all ambiguity, in determining longitude, we go on
to reckon up to 3600 toward the eaft.
You .will no doubt have the curiofity to know,
why geographers, in fettling the firft meridian, have
agreed to fix on one of the Canary iflands ? I beg
leave to reply, that the intention was to begin with
fettling the limits of Europe toward the weft ; and
as thefe iilands, called the Canaries, and lituated in
the Atlantic ocean,, beyond Spain, toward America,
were ftill confidered as part of Europe, it was thought
proper to draw the firft meridian through the moft
remote of the Canary iflands, that we might be en-
abled to compute the other meridians without inter-
ruption, not only all over Europe, but through the
whole extent of Afia : from whence, going on to
reckon toward the eaft, we arrive at America, and
thence return at length to the firft meridian.
But to which of the Canary ides lhall we give the
preference? Certain geographers of France made
choice of the ifle of Ferro3 and the Germans that of
Tenerine,
FIRST MERIDIAN. ivg
Teneriffe, becaufe the real fituation of thefe ifles was
not then fufficiently afcertained, and it was not per-
haps known which of them was the moft remote ;
befides, the German geographers imagined that the
mountain named the Peak of Teneriife was pointed
out, as it were, by the hand of Nature for the firft
meridian.
Be this as it may, it feems rather ridiculous to
draw the firft meridian through a place whofe real
pofition on the globe is not perfectly determined^
for it was not till very lately that the fituation of the
Canaries was afcertained. For this reafon, the moft
accurate aftronomers fix the firft meridian precifcly
20 degrees diftant from that of the obfervatory at
Paris, without regarding through what fpot the firft
may in that cafe pafs ; and it is undoubtedly the
fureft method that can be adopted : and in order to
determine every other meridian, the fimpieft way is .
to find out its diftance from that of Paris : then if
that other meridian is more to the eaft, you have
only to add to it 20 degrees, in order to have the
longitude of the places fituated under it : but if this
meridian be weftward to that of Paris, you muft fub-
tra& the diftance from 20 degrees: finally, if this
diftance toward the weft is more than 20 decrees,
you fubtract. it from 380 degrees, that is, from 20
degrees above 360, in "order to have the longitude of
the meridian.
Thus the meridian of Berlin beino; to the eaftward
of the meridian of Paris n° f 15", the longitude of
310 7/ 25''; and this is likewife the
longitude
iyo FIRST MERIDIAN.
longitude of all other places fituated under the fame
meridian with Berlin.
In like manner the meridian of Peterfburg being
28 degrees more to the eaft than that of Paris, the
longitude of Peterfburg will be 480.
The meridian of St. James's, London, is more to
the weft than that of Paris by 20 25' 15"; fubtrac~t-
ing, therefore, that quantity from 200, the remain-
der, 1 70 34/ 45//, gives the latitude of St. James's,
London.
Let us now take the city of Lima in Peru, the
meridian of which is 700 9' 30" to the weftward of
that of Paris ; that diftance muft be fubtracled from
380 degrees ; which will leave a remainder of 3090
50' 3o//, the longitude of Lima.
Now, when the latitude and longitude of a place
are known, we are enabled to afcertain its true po-
iition on the terreftrial globe, or on a map : for as
the latitude marks the parallel, under which the place
is fituated, and the meridian gives the meridian of
the fame place, the point where the parallel interfects
the meridian, will be exactly the place in queftion.
You have but to look at a map, that of Europe for
example ; and you will fee the degrees of the parallels
marked on both fides, or their diftances from the
equator : above and below are the degrees of longi-
tude, or the diftances of the feveral meridians from
the firft.
The parallels and meridians are ufually traced on
maps degree by degree, fonletimes at the diftance of
5 degrees from each other. In moil maps the meri-
dians
OF DETERMINING THE LATITUDE. l'/I
dians are drawn up and down, and the parallels from
left to right : the upper part is directed toward the
north; the under to the fouth : the right-hand fide
toward the eaft, and the left-hand fide toward the
weft.
It is likewife to be remarked, that as all the meri-
dians meet at the two poles, the more any two meri-
dians approach to either of the poles, the fmaller their
diftance becomes ; at the equator their diftance al-
ways is great eft. Accordingly on all good maps,
where the meridians are traced, you will obferve
that they gradually approximate toward the top, that
is the north, and their diftances increafe as you pro-
ceed toward the equator. This is all that feems to
be requifite for the underftanding of geographical
charts, by means of which an attempt is made to re-
prefent the furface, or part of the furface, of the
globe.
But my principal object was to demonftrate how
the real pofition of every fpot on the globe is deter-
mined by its latitude and longitude.
ifi September, 1 761.
s®-3C-e<
LETTER XLV.
Method of determining the Latitude, or the Elevation of
the Pole.
IT being a matter of fuch importance to know the
latitude and longitude of every place, in order to
afcertain exactly the fpot of the globe where you are,
you
172 OF DETERMINING THE LATITUDE.
you muft be fenfible that it is equally important to
difcover the means of certainly arriving at fuch know-
ledge.
Nothing can be more interefting to a man, who
has been long at fea, or after a tedious journey
through unknown regions, than to be informed at
what precife fpot he is arrived; whether or not he
is near fome known country, and what courfe he
ought to purfue in order to reach it. The only
means of relieving fuch a perfon from his anxiety
would undoubtedly be to give him the latitude and
longitude of the place where he is : but what muft
he do to attain this moft important information ?
Let us fuppofe him on the ocean, or in a vaft defert,
where there is ho one whom he could confult. After
having afcertained, by the help of a terreitrial globe,
or of maps, the latitude and longitude of the place
where he is, he will with eafe, from them, determine
his prefent pofition, and be furnifhed with the ne-
cefiary information refpecting his future progrefs.
I proceed, therefore, to inform you, that it is by
aftronomy chiefly we are enabled to determine the
latitude and longitude of the place where we are ;
and that I may not tire you by a tedious detail of
all the methods which aftronqmers have employed
for this important purpofe, I mall fatisfy my felt with
preferring a general idea of them, flattering myfelf
that this will be fufficient to convey to you the know-
ledge of the principles on which every method is
founded.
I begin with the latitude, which is involved ' \n
fcarcelv
OF DETERMINING THE LATITUDE. I 73
fi.arcely any difficulty, whereas the determination of
the longitude feerhs hitherto to have defied all human
refearch, efpecially at fea, where the utmoft precifion
is requilite. For the difcovery of this laft, accord-
ingly, very confiderable prizes have been propofed,
as an encouragement to the learned to direct their
talents and their induftry toward a difcovery fo in-
terefting, both from its own importance, and from
the honour and emolument which are to be the fruit
of it.
I return to the latitude, and the means of afcer-
taining it, referring to fome future opportunity a
more ample difcuffion of the longitude, and of the
different methods of difcovering it, efpecially at fea.
Let the points B and A (plate I>fg- S-J t>e the poles
of the earth ; B A its axis, and C its centre ; let the
femicircle BDA reprefent a meridian, interfecled by
the equator at the point D ; and BD, AD, will be
each the quadrant of a circle, or an arch of 90 de-
grees : the Uraight line DC will therefore be a radius
of the equator, and DE its diameter.
Let there now be afiumed in this meridian BDA,
the point L, the given place, of which the latitude is
required, or in other words, the number of degrees
contained in the arch LD, which meafures the diilance
of the point L from the equator ; or again, drawing
the radius CL, as the arch LD meafures the angle
DCL, which I mall call y, this angle y will exprefs
the latitude of the place L, which we want to find.
Now it. being iiupoflible to place ourfelves at the
centre
174 0F DETERMINING THE LATITUDE.
centre of the earth, thence to take the meafure of
that angle, we muft have recourfe to the heavens.
There the prolongation of the axis of the earth AB
terminates in the north pole of the heavens P, which
we are to conlider as at an immenfe diftance from
the earth. Let the radius CLlikewife be carried
forward till it terminate in the heavens at the point
Z, which is called the zenith of the place ; then,
drawing through the point L the ftraight line ST
perpendicular to the radius CL, you will recollect-
that this line ST is a tangent of the circle, and that
confequently it will be horizontal to the place L:
our horizon always touching the furfacc of the earth
at the place where we are.
Let us now look from L toward the pole of the
heavens P, which being infinitely diftant, the ftraight
line LQ directed to it, will be parallel to the line
ABP, that is to the axis of the earth: this pole of
the heavens will appear, therefore, between the zenith
and the horizon LT, and the angle TLQ, indicated
by the letter m, will fhew how much the ftraight
line L Q, in the direction of the pole, is elevated above
the horizon ; hence this angle m is denominated the
elevation of the pole.
You have undoubtedly heard frequent mention
made of the elevation of the pole, or, as fome call
it, the height of the pole ', and which is nothing elfe
but the angle formed by the ftraight line LQ in the
direction of the pole, and the horizon of the place
where we are. You have a perfect comprehenfion
6 of
Or DETERMINING THE LATITUDE. 1 75
of the poflibiiity of meafuring tins angle ??i by means
of an agronomical inftrument, without my going
into any farther detail.
Having meafured this angle m, or the height of the
pole, it will give you prccifely the latitude of the
place I., that is the angle y. To make this appear,
it is only neceflary to demonflrate that the two
angles m and y are equal.
Now the line LQ being parallel to CP, the angles
?n ,and n are alternate, and confequently equal. And
the line LT being perpendicular to the radius CL,
the angle CLT of the triangle CLT muft be a right
angle, and the other two angles of that triangle ?i and
x muft be together equal to a right angle. But the
arch BD being the quadrant of a circle, the angle
BCD muft likewife be a right angle ; the two angles
x and y, therefore, are together equal to the two
angles n and x. Take away the angle x from both,
and there will remain the angle y equal to the angle
n ; but the angle n has been proved equal to the angle
m, therefore the angle y is likewife equal to the angle m.
It has already been remarked, that the angle y ex-
preffes the latitude of the place L, and the angle m the
elevation or height of the pole at the fame place L ;
the latitude of any place therefore is always equal to
the height of the pole at that fame place. The means
which ailronomy fupplies, for obferving the height
of the pole, indicate, therefore, the latitude required.
Aftronomical obfervations made at Berlin have ac-
cordingly informed us, that there the height of the
pole
37 5 KNOWLEDGE OF THE LONGITUDE;
pole is 5^9 31', and hence we conclude that the lati-
tude of that city is likewife 52° 31'j
This is one very remarkable inftance to demon-
Urate h'ow the heavens may afiift us in the attainment
of the knowledge of objects which relate only to the
earth.
c^ib September, f]fjl.
LETTER XLVI.
Knowledge of the Longitude, from a Calculation of the
Direction, and of the Space pajed through.
1 NOW proceed to the longitude j and remark that,
on taking a departure,, whether by land or water,
from a known place, it would be eafy to afcertain
the fpot we had reached, did we know exactly the
length of the road, and the direction which we pur-
sued. This mighty in fuch a cafe, be effected even
without the aid of aftronomy 5 and this obliges me
to enter into a more particular detail on the fubject,
We meafure the length of a road by feet ; we
know how many feet go to a mile, and how many
miles go to an arch of one degree upon the globe :
thus we are enabled to exprefs in degrees the diftance
we have travelled.
As to the route or direction in which we travel,
it is neceflary accurately to know the pofition of the
meridian at every place where we are. As the me-
ridian proceeds in one direction toward the north
pole,
• KNOWLEDGE OF THE LONGITUDE. IJJ
pole, and in the other toward the fouth ; you have
only to draw, on the horizon of the fpot where you
are, a ftraight line from north to fouth, which is called
the meridian line of that place. All poflible care mull
be taken to trace this meridian line very accurately,
and here the heavens muft again perform the office
of a guide.
You know it is mid-day when the fun is at his
greateft elevation above the horizon ; or, which is
the fame thino:, the direction of the fun is then ex-
actly fouth, and the fhadoW of a ftaff fixed perpen-
dicularly on a horizontal plane will fall, at that in-
ftant, precifely northward. Hence it is eafy to com-
prehend, how an obfervation of the fun may furnifh
us with the means of accurately tracing a meridian
line, wherever we may be.
Having traced a meridian, every other direction
is very ealily determined.
Let the ftraight line NS (plate 1. fig. 6. J be the
meridian, one of the extremities N being directed
toward the north, and the other S toward the fouth.
With this meridian let there be drawn at right
angles the ftraight line EW, whofe extremity E
fhall be directed toward the eaft, and the other ex-
tremity W toward the weft. Having divided the
circle into 16 equal parts, we fhall have fo many
different directions, denominated according to the
•letters affixed to them ; and in cafe of not purfuing a
direction which exactly correfponds with feme one
of the fixteen, the angle muft be marked which that
Vol. II. N deviating
I78 KNOWLEDGE OF THE LONGITUDE.
deviating line of direction makes with the meridian
NS, or with EW, which is perpendicular to it.
It is thus we are enabled to determine exactly the
direction which we purfue in travelling ; and fo long
as we are allured of the length of the way, and of
the direction purfued, it will be very eafy to afcer-
tain the true place at which we have arrived, and
to indicate both its longitude and latitude. We em-
ploy, for this purpofe, an accurate map, which con-
tains the point of departure, and that which we have
reached ; and by means of the fcale, which gives the
quantity of miles or leagues that go to a degree, it
is eafy to trace, on fuch map, the track purfued and
completed.
Figure 7. of plate L reprefents a map, on which are
marked from left to right the degrees of latitude,
and thofe of longitude from top to bottom ; it is
likewife vifible, on the face of it, that the meridians
converge as they approach toward the north, and
retire from each other toward the fouth, as is the
actual cafe on the globe.*
This map contains part of the furface of the earth,
from the 53d degree of north latitude to the 59th
degree ; and from the 13 th degree of longitude to
the 26th.
Suppofe, then, I take my departure from the place
* All that the author fays in the fequel on this fubje<5t, is ap-
plicable, ftridtly fpeaking, only to marine charts ; but apparently
he did not think himfelf obliged to enter into any detail on their
particular, conftru&ion. — F, E.
L,
KNOWLEDGE OF THE LONGITUDE. 1 79
L, the longitude of which is 1 6°, and the latitude
$j° 20', and that I proceed in the direction ESE ;
and have travelled a fpace of 75 German miles. In
order to determine the longitude and latitude of the
place I have reached, I draw from the place L the
flraight line LM, making with the meridian 160 16'
the fame angle, which the direction ESE in. the pre-
ceding: figure makes with N. Then on that line I
take, according to the fcale marked on the chart,
LM equal to 75 German miles, and the point M
fhall be the place which I have reached.
I have then only to compare this place with the
meridians and parallels traced on the map, and I
find that it's longitude is 240 nearly ; and on mea-
furing more exactly the part of the degree to be
added to the 24th degree, I find the longitude of the
point M to be 240 4'. As to the latitude, I obferve
it to be between the 55th and 56th degree, and, by
an eafy computation, I find it to be 55 ° 25' j fo that
the latitude of the place M, which I have reached, is
550 25', and its longitude 240 4/.
It has here been mppofed that I have invariably
purfued the fame direction ESE, from firft to laft :
but if I have from time to time deviated from that
direction, I have only to perform the fame operation
on each deviation, to find the place where I then
was ; from this I take a frefli departure, and trace
my direction till another deviation takes place, and
fo on, till I reach my object. By thefe means it is
always in my power, whether travelling by fea or
land, to afcertain the place I have reached ; pro-
N 2 vided
TBO KNOWLEDGE OF THE LONGITUDE.
vided I know exactly, through my whole progrefs,-
the direction I purfue, and meafure with equal ac-
curacy the length of the way.
We might in this cafe difpenfe even with the af-
fiftance of aftronomy, unlefs we had occaiion for it
accurately to determine our direction, or the angle
which it makes with the meridian; but the magnetic
needle or compafs may, in many cafes, fupply this
want.
You muft be fenfible, however, that it is poffible
to make a very considerable miftake both in the
computation of the direction, and of the length of
the way, efpecially in very long voyages. How often
is it neceffary to change the direction in travelling
even from hence to Magdeburg ? and how is it pof-
fible to meafure exactly the length of the way? But
when we travel by land, we are not reduced to this
expedient : for we are enabled to meafure by geo-
metrical experiments the diftance of places, and the
angles which the diftances make with the meridian
of every place ; and thus we can determine, with
tolerable accuracy, the true fituation of all places. ,
§tb September, 1761.
LETTER XLVII.
Continuation. Defccls of this Method.
A METHOD of ©bferving the direction purfued,
and the length of the courfe, feems to be of
lingular utility in fea voyages, becaufe there we are
not
KNOWLEDGE OF THE LONGITUDE. ISI
not under the neceflity of deviating from the direc-
tion every moment, as in travelling by land ; for,
with the fame wind, we can proceed in the fame
direction.
Pilots are accordingly very attentive in exactly ob-
ferving the courfe of the veffel, and in meafuring
the progrefs flie has made. They keep an accurate
journal of all thefe obfervations,, at the clofe of every
day, nay (till more frequently ; they trace on their
fea-charts the progrefs they have made, and thus are
enabled to mark on the charts, for every period of
time, the point where they are, and of which they
confequently know the latitude and longitude. Ac-
cordingly, fo long as the courfe is regular, and the
veffel is not agitated by a tempeft, good pilots are
feldom miftaken : but when they are in doubt, they
have recourfe to aftronomical obfervations, from
which they difcover the elevation of the pole ; and
this being always equal to the latitude of the place
where they are, they compare it with that which
they have marked l on the chart, conformably to the
computation of their progrefs. If thefe are found to
coincide, their computation is juft ; if they difcover
a difference, they conclude with certainty that fome
error has been committed, in the computation of
the diftance, and of the courfe j in that cafe, they
re-examine both the one and the other more care-
fully, and endeavour to apply the neceffary correc-
tions, in order to make the computation agree with
the obfervation of the height of the pole, or of the
latitude, which is equal to it,
N 3 This
1 82 KNOWLEDGE OF THE LONGITUDE.
This precaution may be mfficient in Ihort voyages,
as the errors committed can in thefe be of no- great
importance ; but in very long voyages, thefe flight
miftakes may accumulate to fuch a degree, that, at
laft, a very grofs miftake may be committed, and
the place where the veflel actually is may differ con-
iiderably from what it was fuppofed to be on the
chart.
I have hitherto gone on the, fuppofition that the
voyage proceeded quietly ; but fhould a ftorm arife,
during which the veflel is fubjected to the rudeft
concuflions of wind and waves,' it is evident that
the computation of diftance and courfe is entirely
deranged, and that it is impoflible to trace on the
chart the progrefs fhe has made.
It would be very eafy, after this derangement, to
afcertain, by aftronomical obfervations, the latitude
of the fliip's place ; but this would determine only
the parallel of that place, and it would remain totally
uncertain at what point of the parallel flie actually
was.
It is neceffary, therefore, to difcover likewife the
longitude of the place, which fhews us the meridian
under which it is lituated j and then the interfection
of that meridian with the parallel found, will give
the veflel's true place. This will make you fenfible
of what importance it is to aflift mariners in difco-
vering likewife the longitude of the place where
they are.
This neceflity is impofed not only from the con-
iideration of the tempefts to which navigation is li-
able j
KNOWLEDGE OF THE LONGITUDE. 1 83
able ; for it is pofftble, fuppofing the voyage to pro-
ceed ever fo quietly, to be grofsly miftaken in the
computation of both courfe and diftance. Could we
fuppofe the fea to be at reft, it might bcpoffible to
invent various methods of afcertaining, with tole-
rable exactnefs, the way which the veffel has made ;
but there are rapid currents in many places of the
ocean, which have the refemblance of a river run-
ning in a certain direction. Thus it is obferved,
that the Atlantic ocean has a perpetual current into
the Mediterranean fea, through the ftraits of Gib-
raltar ; and that the ocean, between Africa and
America, has a very confiderable current from eaft
to weft, fo that a voyage to America is performed
in much lefs time than a voyage from America to
Europe.
Were fuch currents conftant and well known, we
fhould have confiderable affiftance toward forming
our calculations : but it has been obferved, that they
are fometimes more, fometimes lefs rapid, and that
they frequently change their direction ; which de-
ranges the calculations of the moft fkilful navigator
to fuch a degree, that it is no longer fafe to truft
them. We have but too many fatal inftances of
Jhips dafhed on concealed rocks, and loft, becaufe
thefe were computed to bflftill at a confiderable dif-
tance. It was afterwards difcovered, when too late,
that thefe calamities had been occaiioned by the cur-
rents of the ocean, which deranged the calculations!
of navigators.
In fad, when the ocean has a current which makes
N 4 it
104 KNOWLEDGE OF THE LONGITUDE.
it flow like a river, following a certain direction,
vefiels caught in it are carried away imperceptibly.
In a river we clearly perceive that the current is car-
rying us along, by obferving the banks or the bot-
tom : but at fea no land is vifible, and the depth is
too great to admit, of our making any obfervation
from the bottom. At fea, then, it is impoflible to
difcern the currents ; and hence fo many dreadful
miftakes, refpecting both courfe and diftance. Whe-
ther, therefore, we take tempefts into the account,
or not, we are always under the neceffity of falling
on other methods of afcertaining the longitude of
the places where we may arrive ; and of the various
methods hitherto employed for acquiring this know^
ledge of the longitude, I now proceed to inform
you.
lltb September, 1761.
LETTER XLVIII.
Second Method of determining the Longitude, by Means
of mi exacl'Time Piece.
AVERY fure method of finding the longitude,
would be a clock, watch, or pendulum, fo
perfect, that is to fay, which fhould always go fo
equally, and fo exactly, that no concuffion fhall be
able to affect its motion.
Suppofing fuch a time-piece conftru&ed, let us fee
in what manner, by means of it, we fhould be en-
abled to folve the problem of the longitude. We
mull
Yai.JT.
_PZa£eT,
JVhrlARJfoi*
■fyl
J^orO.
23 at is K6
Z? &+ ZJ
S&t-t&A-
KNOWLEDGE OF THE LONGITUDE. I 85
tnuft return, for this purpofe, to the confideration of
meridians, which we are to conceive to be drawn
through every place on the furface of the globe.
You know that the fun feems to defcribe every-
day a circle round the earth, and that, of confe-
quence, he paffes fucceffively over all the meridians
in the fpace of twenty-four hours.
Now, the fun is faid to pafs over, or through a
given meridian, if a ftraight line drawn from the
fun to the centre of the earth C, (plate Lfig. 8. ) pafs
precifely through that meridian. If therefore, in the
prefent cafe, the line drawn from the fun to the
centre of the earth pafs through the meridian BLM A,
we would fay that the fun was in that meridian, and
then it would be mid-day to all the places fituated
under fuch meridian ; but under every other, it
would not be mid-day at that precife inftant ; it
would there be before noon or after it, every where
elfe.
If the meridian BNA is fituated to the ealhvard
of the meridian BMA, the fun, in making his cir-
cuit from eaft to weft, muft pafs over the meridian
BNA before he reaches the meridian BMA; con-
fequentiy it will be mid-day under the meridian
BNA earlier than under the meridian BMA; when,
therefore, it mall be mid-day under this laft meri-
dian, mid-day under every other meridian to the
eaftward will be already paft, or it will be afternoon
with them. On the contrary, it will be ftill fore-
noon under every meridian, fay BDA, fituated to
the
I 86 KNOWLEDGE OF THE LONGITUDE.
the weftward, as the fun cannot reach it till he has
palled over the meridian BMA.
And as the motion of the fun is regular and uni-
form, and he completes his circuit of the globe, that
is 360 degrees, in twenty-four hours, he muft every
hour defcribe an arch of 15 degrees. When, there-
fore, it is noon at Berlin, and at every other place
iituated under the fame meridian, noon will be al-
ready paft under meridians Iituated to the eaftward ;
and more particularly ftill under the meridian Iitu-
ated 1 5 degrees to the eaftward of that of Berlin, it
will already be one o'clock ; under the meridian 30
degrees eaftward, two o'clock ; under that of 45 de-
grees, three o'clock afternoon, and fo on. The con-
trary will take place under meridians Iituated to the
weilward of that of Berlin ; when it is noon there,
it will be only eleven o'clock forenoon under the
meridian 15 degrees to the weftward, ten o'clock
under the meridian of 30, nine o'clock under the
meridian of 45 degrees weftward, and fo on ; a dif-
ference of 1 5 degrees between two meridians always
amounting to. an hour of time.
To elucidate ftill more clearly what has now been
remarked, let us compare the two cities Berlin and
Paris. As the meridian of Berlin is n° iy/ 1 5", to
the eaftward of that of Paris, reckoning an hour to
15 degrees, this difference of ii° f 15", will give
44 minutes and 29 feconds of time, or three quar-
ters of an hour nearly. When, therefore, it is mid-
day at Paris, it will be 44 minutes and 29 feconds
after
KNOWLEDGE OF THE LONGITUDE. iSy
after mid-day at Berlin ; and reciprocally, when it
is mid-day at Berlin, it will only be i 5 minutes and
3 1 feconds after eleven o'clock at Paris : fo that it
will not be noon at this laft city till 44 minutes and
29 feconds afterwards. Hence it is evident that the
clocks at Berlin mould always be falter than thofe of
Paris, and that this difference ought to be 44 mi-
nutes and 29 feconds.
The difference between the meridians of Berlin
and Magdeburg is i° 40', Berlin therefore is to the
eaftward of Magdeburg j and this difference reduced
to time gives 6 minutes and 40 feconds, which the
clocks of Berlin ought to indicate more than that
of Magdeburg. Confequently, if it is juft now noon
at Magdeburg, and the clocks there, which I fup~
pofe well regulated, point to XII. the clocks at Ber-
lin ihould, at the fame inftant, indicate 6 minutes
and 40 feconds after XII, that is, noon there is al-
ready pad.
Hence you fee, that in proportion as places differ
in longitude, or as they are fttuated under different
meridians, well regulated time-pieces ought not to
point out the fame hour at the fame inftant, but the
difference ought to be a whole hour, when that of
the longitude is 1 5 degrees.
In employing a time-piece then for afcertaining the
longitude of the places through which we pafs, it,
would firft be neceffary to regulate it exactly at fome
place where we actually were. This is done by ob-
ferving the inftant of noon, that is the inftant when
the fun paffes over the meridian of that place j and
the
I 88 KNOWLEDGE OF THE LONGITUDE.
the time-piece ought then to point precifely to XII,
It ought afterwards to be adjufled in fuch a manner,
that always after a revolution of 24 hours., when the
fun returns to the meridian, the index, after having
made two complete circuits, mould again point ex-
actly to XII. If this is carefully ohferved, fuch well
regulated time-pieces will not coincide in different
places, unlefs thefe be fituated under one and the fame
meridian ; but if they are fituated under difFerent
meridians, that is if there be a difference of longi-
tude, the time indicated by the clock or watch, at
the fame moment, will likewife be different ; at the
rate of one whole hour of time for every 1 5 degrees
of lonsritude. '•'*
o
Knowing then the difference of time, indicated by
well regulated time-pieces, at different places, and
at the fame mflant, we are enabled exactly to com-
pute the difference of longitude at thefe two places,
reckoning always 15 degrees for an hour, and the
fourth part of a degree for a minute.
lyth September ", 1761.
LETTER XLIX.
Continuation, and farther Elucidations.
7"OU will be lefs furprifed at the difference- of
time which well regulated time-pieces mult in-
dicate, under different meridians, when you reflect,
that while it is noon with us, there are countries to-
ward the ealt, where the fun is already fet, and that
there
KNOWLEDGE OF THE LONGITUDE. I 89
there are others toward the weft, where he is but
juft rifing. It: muft therefore be already night with
the one, and ftill morning with the other, at the
fame inftant that it is noon with us. You know,
befides, that with our antipodes, who are under the
meridian diametrically oppofite to ours, it is night,
while it is day with us j fo that our noon correfponds
exactly to their midnight.
- It will be an eafy matter, after thefe elucidations,
to fhew how an exact time-piece may affi.il us in dis-
covering the difference of meridians, or that of the
longitude, at different places.
Suppofmg me poffeffed of fuch ari excellent time-
piece, which, once exactly regulated, fhews me every
day the precife time* it is at Berlin, fo that when-
ever it is noon at Berlin, it points precifcly to XII. :
fuppofing farther, that it goes fo regularly, that once
adjufted, I have no farther occaiion to touch it, and
that it's motion is not to be deranged either by the
fhaking of a carriage, or the agitation of a vefiel on
the ocean, or by any concuflion whatever to which
it may be expofed.
Provided thus, with a time-piece of this defcrip-
tion, I fet out to travel, whether by land or by fea ;
perfectly affured that, go where I will, it's motion will
be fteady and uniform, as if I had remained at Berlin :
it will every day point to XII. at. the very moment
* We muft Here underftand the mean (in French moyen) time*
• whole relation to the true time is laid down in attronomicai tables
The author deemed it unnecessary here to point out that diflinc-
tion, as it would have led to a detail too minute. — F. F .
it
lf)0 KNOWLEDGE OF THE LONGITUDE.
it is noon at Berlin, and that, wherever I may happen
to be. On this journey, I arrive nrfl at Magdeburg:
there I obferve the fun when he paries the meridian,
and this happens when he is exactly fouth ; and it
being then noon at Magdeburg, I confult my time-
piece, and obferve it points to 6 minutes and 40 fe-
conds after XII. : whence I conclude, that when it is
noon at Magdeburg, noon at Berlin is already pa ft,
and that the difference is 6^ 40'', of time, which cor-
refpond to i° 40' of diftance ; therefore the meridian
of Magdeburg is to the weftward of that of Berlin.
The longitude of Berlin, therefore, being 310 f 15",
the longitude of Magdeburg will be i° 40' lefs, that
is, it will be 290 27' 15".
I thence proceed to Hamburgh, accompanied by
my time-piece, which I never touch ; and there, ob-
ferving when it is noon by the fun, for I cannot de-
pend on the public clocks which there announce the
hour, I find my time-piece already announces 13' 33*
after XII.; io that at Berlin noon is paifed 13' 33"
when it is exactly noon at Hamburgh ; hence I con-
clude, that the meridian of Hamburgh is 30 23' 15"
to the weftward of that of Berlin ; reckoning 1 50, to
an hour, that is one degree for every 4 minutes of
time; accordingly I find that 13' 33" of time give
30 2^ iy of diftance, for the difference of the me-
ridians. The longitude of Hamburgh will be, of
courfe, 270 44'.
At Hamburgh I go to fea, ftiil accompanied by my
time-piece, and after a long voyage I arrive at a place
where, waiting for noon, the moment of which I ;
afcertain
KNOWLEDGE OF THE LONGITUDE. I$I
afcertain by obferving the fun, I find that my time-
piece indicates only 58' 15" after X. fo that then it
is not yet noon at Berlin, and the difference of time
is 1 hour i' 45", from which I conclude, that the
place at which I have arrived is to the eaftward of
Berlin ; and as one hour gives 1 5 degrees, one mi-
nute of time 15', and 45 feconds of time 1 1' 15",
the difference of the meridians will therefore be 1 50
s6/ 1 5". I find then that I am at a place to the eaf -
ward of Berlin, whofe longitude is greater than that
of Berlin by 150 26' 15" ; now the longitude of that
city being 310 y/ 15", the longitude of the place
where I am rauft be 46° 33' 30". Thus I have dis-
covered under what meridian I now am, but I am
ftill uncertain as to the point of the meridian. In
order to afcertain this I have recourfe to aftronomi-
cal obfervations, and find the height of the pole to
be precifely 410. Knowing likewife that I am ftill in
the northern hemifphere, as I have not paffed the
equator, I difcover that I actually am at a place whofe
latitude is4i° north, and the longitude 460 33' 30''.
I take therefore my globe, or maps, and trace the
meridian whofe longitude is 460 33' 30''; I look for
the place whofe latitude is 410, and at the point of
interfeclion I find I have got to the city of Conftan-
tinople, without having occafion to apply for infor-
mation to any perfon whatever.
Thus, at whatever place of the globe I may ar-
rive, poflefied of a time-piece fo exact, I am able to
afcertain the longitude of it, and then an observation
of the height of the pole will mew me it's latitude.
All that remains therefore is to take the terreftrial
7 globe,
I92 KNOWLEDGE OF THE LONGITUDE.
globe, or a good map, and it will be eafy for me to
ascertain where I am, however unknown to me the «
country may in other refpeeis be.
It is much to be regretted, that artifts of the
greateft ability have hitherto been unfuccefsful in the
construction of time-pieces fuch as I have defcribed,
and fuch as the cafe requires. We meet with a great
many very good pendulum machines, but they go
regularly only when fixed in undifturbed Situations j
the flighteft concuffion is apt to derange their motion ;
they are therefore totally ufelefs in long fea voyages.
It is obvious that the pendulum, which regulates the
motion, is incapable of refilling the fhocks to which
it is expofed in navigation. About ten years ago,
however, an Englifh artift pretended that he had
conftructed a time-piece proof againft the motion of
a fhip at fea, and that after having tried it a long
time together in a carriage on the road, it was im-
poflible to perceive the flighteft derangement : on
which the inventor claimed, and received part of the
parliamentary prize propofed for the difcovery of the
longitude, and the reft was to be paid, after it had
been put to the proof of a long voyage. But fince
that time we have heard no more of it ; from which
it is to be prefumed that this attempt top has failed,
like many others which had the fame object in view*.,
\yth September, 1761.
* The Author is here undoubtedly alluding to Mr. Harrifon,
who fe marine time-piece has been tried with fuccefs in England,
Meflrs. le Roy and Bertbout have, in France, approved their talents
in tiie lame way, — E. Er
LETTER
KNOWLEDGE OF THE LONGITUDE. 1 93
LETTER L.
Eclipfes of the Moon, a Third Method of finding the
Longitude,
FROM want of the exquifite time-piece, of which
I have endeavoured to give you an idea, the
eclipfes of the moon have hitherto been conlidered
as the moil certain method of difcovering the longi-
tude; but thefe phenomena prefent themfelves fo
rarely, that we have it not in our power to employ
them fo often as occaiion requires.
You know that the moon is eclipfed, when it paffes
into the fhadow of the earth : it is poffible, then, to
obferve the moment when the moon begins to enter
into the made, and when me has emerged ; the one
is denominated the beginning of the eclipfe, and the
other its end ; and when both are obferved, the
mean time betwixt them is denominated the middle
of the eclipfe. The moon is fometimes wholly im-
merged in the fhadow of the earth, and remains for
fome time invifible ; this we call a total eclipfe, during
which we may remark the moment when the moon
entirely difappears, and that when fhe begins to
emerge; the former is called the beginning of total
darknefs, and the latter, the end of it. But when a
part only of the moon is obfeured, we call it a partial
eclipfe, and we can remark only the moment of its
beginning and ending. You know likewife that
Vol. II. O eclipfes
194 KNOWLEDGE OF THE LONGITUDE.
cclipfes of the moon can happen only at the full, and
that but rarely.
When, therefore, an eclipfe of the moon is ob~
ferved at two different places fituated under differe t
meridians, the beginning of the eclipfe will be clearly
feen at both, and at the fame inftant, but the time-
pieces at thefe different places will by no means indi-
cate the fame hour, or any other divifion of time ex-
actly the fame : I mean well regulated time-pieces,
each of which points precifely to XII. when it is noon
at that place. If thefe places are fituated under the
fame meridian, their time-pieces will no doubt indi-
cate the fame time at the beginning and at the end of
the eclipfe. But if thefe two meridians are 1 5 de-
grees diftant from each other, that is, if the difference
of their longitude be 150, the time-pieces mull differ
a complete hour, from the beginning to the end of
the eclipfe ; the time-piece of the place fituated to the
eaflward will indicate one hour more than the other j
the difference of 300 in longitude will occafion that
of two hours in the time indicated by well regulated
clocks or watches ; and fo on, according to the fol-
lowing table.
DIFFERENCE
KNOWLEDGE OF THE LONGITUDE.
^95
DIFFERENCE OF LONGITUDE.
of Degr
ses. of Time.
15°
i hour.
3o°
2.
45°
.3-
60°
4.
75°
5-
90°.
6.
105=
7-
120°
8.
135°
9.
1 500
10.
165°
11.
i8o0
12.
If therefore the difference of longitude were 15c,
the time-pieces would differ 10 hours from the be-
ginning to the end of the eclipfe.
Thus when the fame eclipfe is obferved at two
different places, and the moment of it's commence-
ment is exactly marked on the time-pieces at each,
it will be eafy to calculate, from the difference of
the time indicated, the difference of longitude be-
tween the two places. Now, that where the time is
more advanced, mull be fituated more toward the
eaft, and confequently it's longitude greater, as lon-
gitude is reckoned from weft to eaft.
By fuch means, accordingly, the longitude of the
principal places on the globe have been determined,
O 2 and
19.6. KNOWLEDGE OF THE LONGITUDE*
and geographical charts are conftructed conformably
to thefe determinations. But it is always neceffary
to compare the obfervations made, in a place the lon-
gitude of which was not already known, with thofe
which had been made, in a known place, and to wait
the refult of that comparifon. Were I to arrive then,
after a long voyage, at an unknown place, and an
opportunity prefented itfelf of there obferving an
eclipfe of the moon ; this wrould, in the firft inflance,
afford me no afliflance toward the difcovery of the
longitude of that place ; I could not till after my re-
turn compare my obfervation with another made in
a known place, and thus I mould learn too late where
I was at that time. The grand point in requeft is,
How am I, at the moment, to acquire the neceffary
information, that I may take my meafures accord-
ingly ?
Now the motion of the moon being fo exactly
known, it is poffible to attain this fatisfa&ion, for we
are thereby enabled not only to calculate before-hand
all future eclipfes, but to afcertain the moment of
the beginning and end, according to the time-pieces
of a given placev You know that our Berlin alma-
nacks always indicate the beginning and the end of
every eclipfe viftble at that city. In the view, then,
of undertaking a long voyage, I can furnifh myfelf
with a Berlin almanack, and if an opportunity pre-
fents itfelf of obferving an eclipfe of the moon at an
unknown place, I muft mark exactly the time of it,
by a time-piece accurately regulated by the fun at
noon, and compare the moments of the beginning;
and
KNOWLEDGE OF THE LONGITUDE. 1 97
and end of the eclipfe with thofe indicated in the
almanack, in order to afcertain the difference be-
tween the meridian of .Berlin, and that which paffes
through the place where I am.
But befide the rarity of eclipfes of the moon, this
method is fubjecl: to a farther inconvenience; we are
not always able to diftinguifh, with fufficient accu-
racy, the moment of the beginning and end of the
eclipfe, which comes on fo imperceptibly that a mif-
take of feveral feconds may very eafily be committed.
But as the miftake'will be nearly the fame at the end
as at the beginning, we calculate the middle point of
time between the two moments obferved, which will
be that of the eclipfe, and we afterward compare
this with that which is indicated by the almanack
for Berlin, or for any other known place.
If the almanack for next year mould not be pub-
Hfhed, when I fet out on my voyage, or fuppoling it
to laft more years than one, there are books contain-
ing the eclipfes calculated for feveral years to come,
2,zd September , 1761.
!>©•?£•««
LETTER LI,
Obfer-vation of the Eclipfes of the Satellites of Jupiter-, a
Fourth Method of finding the Longitude.
ECLIPSES of the fun may likewife affift in afcer-
taining the longitude, but in a way that re-
quires more profound refearch, becaufe the fun i&
not immediately obfeured ; it is only the interpofu
O 3 tion
I98 KNOWLEDGE OF THE LONGITUDE.
tion of the body of the moon, which obftrucfcs the
tranfmiflion of his rays to us ; as when we employ
a parafol to fhelter us from them, which prevents
not others from beholding all their luftre. For the
moon conceals the fun only from part of the inha-
bitants of the earth ; and an eclipfe of the fun may
be clearly vifible at Berlin, while at Paris there is no
interception of his light.
But the moon is really eclipfed by the fliadow of
the earth ; her own light is diminiflied or extin-
guished by it ; hence the eclipfes of the moon are
feen in the fame manner, wherever fhe is above the
horizon at the time of the eclipfe.
It cannot have efcaped your penetration, that if
there were other heavenly bodies which, from time
to time, underwent any real obfcuration, they might
be employed with fimilar fuccefs, as the eclipfes of
the moon, in afcertaining the longitude. The fatel-
Htes of Jupiter, which pafs fo frequently into the
fhadow of their planet, that almofl every night one
or other of them is eclipfed, may be ranked in the
number of thefe, and furnifh us with another excel-
lent method of determining the longitude. Aftro-
nomers accordingly employ it with great fuccefs.
You know that Jupiter has four fatellites, which
make their revolutions round him, each in his own
orbit, as reprefented in the annexed figure (plate II,
Jig. 1.) by circles defcribed round Jupiter. I have
Ukewife reprefented the fun in this figure, in order
to exhibit the fhadow A OB behind the body of Ju-
piter. You fee the firft of thefe fatellites, marked 1,
on
KNOWLEDGE OF THE LONGITUDE. I 99
on the point of entering into the Shadow ; thje fe-
cond, marked 2, has juft left it ; the third, 3, is
Still at a great diftance, but approaching to it ; and
the fourth, 4, has left it a considerable time ago.
As foon as one of thefe Satellites panes into the
made, it becomes invifible, and that Suddenly ; fo
that at whatever place of the globe you may happen
to be, the Satellite which was before distinctly vifible,
difappears in an inftant. This entrance of a fatellite
into the Shadow of Jupiter is denominated immerfion9
and it's departure from the Shade emerjion \ when the
fatellite, which had for Some time been invifible, Sud-
denly re-appears.
The immerfions and emerfions are equally adapted
to the determination of the longitude, as they take
place at a decided inftant ; fo that when Such a phe-
nomenon is obServed at Several places of the globe,
you muft find, in the time indicated by the time-
pieces of each, the difference which exactly corre-
fponds to the difference of the diftance of their me-
ridians. Is is the fame thing as if we obServed the
beginning or the end of an eclipfe of the moon ; and
the cafe is then involved in no difficulty. For fome
time paft we have been able to calculate theSe eclipfes
of the fatellites of Jupiter, that is their immerfiohs
and emerfions ; and we have, only to compare the
time obServed, with the time calculated for a given
place, fay Berlin, in order to conclude, at once, the
diftance of it's meridian from that of our capital.
This method is accordingly pra&ifed univerfally-
in travelling by land : but the means have not yet
O 4 been
£00 KNOWLEDGE OF THE LONGITUDE.
been difeovered of profiting by it at fea, where, how-
ever, it is of Hill greater importance for a man to
know with certainty where he is. Were the fatel-
lites of Jupiter as vifible to the nakecf eye as the
moon is, this method would be attended with no
difficulty, even at fea, but the. obfervation cannot be
made without a telefcope of at leaft four or five feet
in length, a circumftance which prefents an infur-
mountable obftacle.
You well know that it requires fome addrefs to
manage, even at land, a telefcope of any length, to
direct it toward the object, which you wifb to con-
template, and to keep it fo fteady as not to lofe the
object : you will eafily comprehend, then, that a fhip
at fea, being in a continual agitation, it muft be al-
moft impoffible to catch Jupiter himfelf 5 and if you
could find him, you would lofe him again in a mo-
ment. Now in order to make an accurate obferva-
tion of the immerfion or emerfion of one of the fa-
tellites of Jupiter, it is abfolutely neceffary that you
mould have it in your power to look at him fteadily
for fome time together, and this being impoffible at
fea, we are, to all appearance, conftrained to aban-
don this method of determining the longitude.
This inconvenience, however, may be remedied
two ways ; the one by the conftruction of telefcopes
fix inches long, or ftill lefs, capable of difcovering
clearly the fatellites of Jupiter;- and there can be no
doubt that thefe would be more manageable than
fuch as are four or five feet in length. Artifts are
actually employing themfelves with fuccefs in bring-
ing
KNOWLEDGE OF THE LONGITUDE. 201
ing telefcopes of this fort to perfection ; but it has
not yet been proved whether or not it will require
as much addrefs to point them to the object, as thoie
which are longer.
The other way would be to contrive a chair, to be
ufed on fhip-board, which mould remain fixed and
motionlefs, fo as not to be affected by the agitation
of the veffel. It does not feem impoffible that a
dextrous mode of balancing might effect this. In
fact, it is not long fince we read in the public prints,
that an Englimman pretended that he had conftrucled
fuch a chair, and thereupon claimed the prize pro-
pofed for the difcovery of the longitude. His claim
was well founded, if he indeed conftructed the ma-
chine, as it would be poflible, by means of it, to
obierve at fea the immerfions and emerfions of the
fatellites of Jupiter, which are undoubtedly very
much adapted to the making of this difcovery : but
for fome time paft no farther mention has been made
of it. From the whole, you muft have perceived to
how many difficulties the difcovery of the longitude
is fubjecled.
z6tb September ; 176 1.
LETTER , LII.
The Motion of the Moon, a Fifth Method.
HE heavens furniili us with one refource more
T
for difcovering the longitude without the af-
fiftance of telefcopes, in which aftronomers feem to
place
202 KNOWLEDGE OF THE LONGITUDE.
place the greateft confidence. It is the moon, not:
only when eclipfed, but at all times, provided fhe be
viiible ; an unfpeakable advantage, confidering that
eclipfes are fo rare, and that the immerfions and
emerfions of the fatellites of Jupiter are of fuch dif-
ficult obfervation : there being a confiderable time
every year, during which the planet Jupiter is not
vifible to us, whereas the moon is aimoft conftantly
in view.
You muft undoubtedly have already remarked,
that the moon rifes every day aimoft three quarters
of an hour later than the preceding, not being at-
tached to one fixed place relatively to the ftars, which
always preferve the fame iituation with refpect to
each other, though they have the appearance of be-
ing carried round by the heavens, to accomplifh
every day their revolution about the earth. I fpeak
here according to appearances ; for it is the earth
which revolves every day round it's axis, while the
heavens and the fixed ftars remain at reft ; while the
fun and planets are continually changing their place
relatively to thefe. The moon has likewife a motion
abundantly rapid from one day to another, with re-
lation to the fixed ftars.
If you were to fee the moon to-day near a certain
fixed ftar, it will appear to-morrow, at the fame
hour, at a confiderable diftance from it, toward the
eaft, and the diftance fometimes exceeds even 15 de-
grees. The velocity of her motion is not always the,
fame, yet we are able to determine it very exactly
for every day j by which means we can calculate
before-
KNOWLEDGE OF THE LONGITUDE. 203
before-hand her true place in the heavens, for every
hour of the day, and for any known meridian, fay
that of Berlin, or Paris.
Suppofe, then, that after a long voyage I find my-
felf at fea, in a place altogether unknown, what ufe
-can I make of the moon, in order to difcover the
longitude of the place where I am ? There is no dif-
ficulty with refpecf. to the latitude, even at fea, where
there are means abundantly certain for afcertaining
the height of the pole, to which the latitude is al-
ways equal. My whole attention, then, will be di-
rected to the moon ; I will compare her with the
fixed flars which are neareft, and thence calculate
her true place relatively to them. You know there
are celeftial globes, on which all the fixed liars are
arranged, and that celeftial charts are likewife con-
structed, fimilar to geographical maps, on which are
reprefented the fixed ftars which appear in a certain
quarter of the heavens. On taking, then, a celeftial
chart, on which the fixed ftars, to which the moon
is near, are marked, it will be an eafy matter to de-
termine the true place where the moon at that time
is ; and my watch, which I have taken care to regu-
late there, from an obfervation of the moment of
noon, will indicate to me the time of my lunar ob-
fervation. Then, from my knowledge of the moon's
motion, I calculate for Berlin, at what hour fhe muft
appear in the fame place where I have feen her. If
the time obferved exactly correfpond with the time
of Berlin, it will be a demonftration, that the place
where I am is precifely under the meridian of Berlin,
and
204 KNOWLEDGE OF THE LONGITUDE.
and that confequently the longitude is the fame,
But if the time of my obfervation is not that of Ber-
lin, the difference will give that which is between
the meridians ; and reckoning 1 5 degrees for every
hour of time, I compute how much the longitude of
the place I am at is greater or lefs than that of Ber-
lin : the place where time is more advanced has al-
ways the greater longitude.
This is an abftract of the manner of determining
longitude by fimple obfervations of the moon. I re-
mark, that- the happieft moments for fuccefefully
performing this operation, and for accurately deter-
mining the moon's place, are, when a fixed liar hap-
pens to be concealed behind her body ; this is called
occultation^ and there are two inftances favourable to
obfervation, that when the moon in her motion
completely covers the liar, and that when the ftar
re-appears. Aftronomers are particularly attentive
to catch thefe inftants of occultation, in order to
calculate from them the moon's true place.
I forefee, however, an objection you will probably
make, refpecting the time-piece with which I fup-
pofe our navigator provided, after having main-,
tained the impoffibility of constructing one that fhall
be proof againft every agitation of a fliip at fea. But
this impoffibility refpects only fuch time-pieces as are
expected to preferve a regular motion for a long
time together, without the neceflity of frequent ad-
justment: for as to the obfervations in queftion, a
common watch is quite fufficient, provided it go re-
gularly for fome hours, after having been carefully
}*j adjufted
KNOWLEDGE OF THE LONGITUDE. 23$
adjufted to the noon of the place where we are : iup-
pofmg a doubt to arife, whether we could calculate
from it the fucceeding evening or night, at the time
we obferve the moon, the ftars likewife will afford
the means of a new and accurate adjuftment. For
as the fituation of the fun, with relation to the fixed
ftars, is perfectly known, for any time whatever,
the fimple obfervation of any one ftar is fuflicient to
determine the place where the fun muft then be ;
from which we are enabled to calculate the hour
that a well-regulated time-piece ought to indicate,
Thus, at the very inftant of making an obfervation
by the moon, we are enabled likewife to regulate
our time-piece by the ftars, and every time-piece is
fuppofed to go regularly for fo fhort a fpace.
' zqth September ; 1761.
LETTER LILT.
Advantages of this lafi Method '; its Degree of
Precijipn.
THIS laft method of finding the longitude,
founded on lunar obfervations, feems to merit
the preference, as the others are fubjecled to too
many difficulties, or the opportunities of employing
them occur too feldom, to be ufeful. And you muft
be abundantly fenfible, that fuccefs depends entirely
On the degree of precifion attained in forming the
calculation, and that the errors which may be com-
mitted would lead to conclufions on which we could
place
2o6 KNOWLEDGE OP* ttlE LONGITUDE*
place no dependence. It is of importance, therefore,
to explain what degree of precifion we may reafon*
ably hope' to be attainable in reducing this method
to practice, founded on the confiderable change
which the moon undergoes, from one day to an-
other, in her pofition. It may be affirmed, that if
the moon's motion were more rapid, it would be
more adapted to the difcovery of the longitude, and
"would procure for us a higher degree of precifion.
But if, on the contrary, it were much flower, fo
that we could fcarcely difcern any change of 'her po-
fition from day to day, we could derive very little,
if any, affiftance from her, toward the difcovery of
the longitude.
Let us fuppofe, then, that the moon changes her
place among the fixed ftars, a fpace of 1 2 degrees in
24 hours ; Ihe will, in that cafe, change it one de-
gree in two hours, and half a degree, or 30 minutes,
in an hour : if we were to commit a miflake in ob-
ferving the moon's place, of 30 minutes, it would
be the fame thing as if we obferved the moon an
hour earlier or later, and we mould commit a mif-
take of one hour in the conclufion, fefpecting the
difference of the meridians. Now, one hour's dif-
ference in the meridians correfponds to 15 degrees
in their longitude ; confequently, we mould be mif-
taken 1 5 degrees in the longitude itfelf of the place
we look for ; which would undoubtedly be an error
fo enormous, that it were almoft as well to know
nothing about it ; and a firnple computation of the
diftan'ce and the direction, however uncertain, could
not
KNOWLEDGE OF THE LONGITUDE. 10j
not pofiibly lead to a miftake fo very grofs. But a
man mull have gone to work in a very flovenly man-
ner, to commit a miftake of 30 minutes refpecting
the moon's place, and the inftruments which he em-
ployed mull have been very bad, a thing not to be
iuppofed.
Neverthelefs, however excellent the inftruments
may be, and whatever degree of attention may have
been bellowed, it is impofiible to keep clear of all
error, and he mull have acquitted himfelf very well
indeed, who has not committed the miftake of one
minute in determining the moon's place. Now, as
it changes half a degree, or 30 minutes, in one hour,
it will change one minute of diftance in two minutes
of time. When, therefore, the miftake of the moon's
place amounts to no more than one minute, the
miftake in the difference of meridians will amount
to two minutes of time. And one hour, or 60 mi-
nutes, being equivalent to 1 5 degrees of longitude,
there will refult from it an error of half a decree in
the longitude, and this point of precifion might be
lufHcient for every purpofe, were it but attainable.
I have hitherto fuppofed our knowledge of the
moon's motion to be fo perfect, that, for a known
meridian, we could determine the moon's true place,
for every moment, without an error ; but we are
ilill very far Ihort of that point of perfection. Within
thefe twenty years, the error in this calculation was
more than fix minutes ; and it is but lately that the
ingenious Profeffor Mayer, at Gottingen, purfuing
the track I had pointed out to him, has mcceeded lb
far
2C8 KNOWLEDGE OF THE LONGITUDE. §
far as to reduce this error to lefs than a minute. It
may very eafily happen, then, that in the calculation
likewife, the error of one minute may be committed ;
which, added to that of a minute committed in the
obfervation of the moon's place, will double that
which remits from it, refpecting the longitude of
the place where we are ; and, confequently, it may
poffibly amount to a whole degree : it is proper far-
ther to remark, that if the moon in 24 hours mould
change her relative fituation more than 1 2 degrees,
the error in the longitude would be lefs confiderable.
The means may perhaps be difcovered of diminifhing
itill farther the errors into which we are liable to
fall, in the obfervation and in the calculation ; and
then we ihould be able to afcertain the longitude to
a degree, or lefs. Nay, we ought not to defpair of
attaining a ftill higher degree of precifion. We have
only to make fever al obfervation s, which can be eafily
done by remaining feveral days together at the fame
place. It is not to be apprehended, in that cafe,
that all the con clufions Ihould be equally defective ;
fome will give the longitude fought too great, others
too fmall, and by ftriking a medium between all the
conclufions, we may reft allured that this longitude
will not be one degree removed from the truth.
The Englifh nation, generoufly difpofed to engage
genius and ability in this important refearch, has
propofed three prizes, for afcertaining the longi-
tude, one of £. 10,000, one of £.-15,000, and one of
£.20,000. The firft of thefe is to be bellowed on
the peribn who lhall determine the longitude to a
degree,
ON THE MARINER'S COMPASS. 200.
degree, or about it ; fo as to give perfect afTurance
that the error fhall not exceed one degree at molt.
The fecond is to be given to him who fhall difcOver
a method ftill more exact, fo as that the error lhall
never exceed two thirds of a degree, or 40 minutes.
The higheft prize is deftined to the man who fhall
afcertain the longitude fo exactly that the error fhall
never exceed half a degree, or 30 minutes : and a
higher degree of precifion is hardly to be expected.
No one of thefe prizes has hitherto been allotted :
I do not take into the account the gratification be-
ftowed on the artift who pretended to it from his
construction of perfect time-pieces. Mr. Mayer is
at this moment claiming the higheft, and I think he
is entitled to it.
id Ofiober, 1761.
1— »©•$?•©<
LETTER LIV.
On the Mariner's Compafs, and the Properties of the
Magnetic Needle,
YOU are by this time fufSciently informed re-
flecting the difcovery of the longitude : I have
had the pleafure of explaining the various methods
which have been employed for the determination of it»
The firft, and mouV natural, is carefully to obferve
the quantity of fpace which we have gone over, and
the direction in which we moved ', but the currents
and tempefts to which fea-voyages are expofed, ren-
der this method impracticable.
Vol. II. P The
2io on the Mariner's compass,-
The fecond requires the conftru&ion of a time*
piece fo perfect as to go always uniformly, notwith-
{landing the agitation of a fliip at fea ; which no ar=
tift has hitherto been able to accomplilh.
The third is founded on obfervation of the eclipfes
of the moon, which would completely anfwer every
purpofe, were not opportunities of employing it too
rare, and leafb in our power, when the neceility may
be mofl urgent.
The fourth refers to the eclipfes of the fatellites of
Jupiter, which would anfwer the purpofe extremely
well, had we the means of employing, at fea, tele-
fcopes of a certain defcription* without which they
are invifible.
Finally, obfervations of the moon herfelf fonifh a
fifth method, which appears the moll practicable,,
provided we were able to obferve the moon's place
in the heavens fo exactly, that the error in calcula-
tion (and error is unavoidable).' fhould never exceed
one minute; in order to be allured that we are not
miftaken above one degree in the determination of
the longitude.
To one or the other of thefe five methods, perfons
engaged in this refearch have chiefly directed their1
fpeculations ; but there is ftill a fixth, which feems
likewife adapted to the folution of the problem, were
it more carefully cultivated j and will perhaps one
day furnifh us with the moll certain method of dis-
covering the longitude j though as yet we are far,
very far, fhort of it.
It is not derived from the heavensybut is attached
to
Ott THE MARINER*S COMPASS. 211
to the earth limply, being founded on the nature of
the magnet, and of the compafs^ The explication
of it opens to me a new field of important phyfical
obfervation, for your amufement and inftruction, on
the fubject of magnetifm, and I flatter myfelf you
will attend with delight and improvement to the
elucidations which I am going to fuggeft.
My reflections mall be directed only to the main
fubject of our prefent refearch, I mean the difcovery
of the longitude. I remark, in general, that the
magnet is a ftone which has the quality of attracting
iron, and of difpofing itfelf in a certain direction ;
and that it communicates the fame quality to iron
and fteel, by rubbing, or limply touching them with
a magnet ; propofing afterwards to enter into a more
minute difcuflion of this quality, and to explain the
nature of it.
I begin, then, with the defcription of a magnetic
needle, which, mounted in a certain manner, for the
ufe of mariners, is denominated the compafs.
For this* purpofe, we provide a needle of good
fteel, nearly refembling fig. i. of plate II. one extre-
mity of which B terminates in a point, the better to
diftinguifh it from the other A ; it is furnifhed at
the middle C with a fmall cap^ hollowed below, for
the purpofe of placing the needle on a pivot or point
D, as may be feen in the fecond figure.
The two ends are adjufted in fuch a manner, that
the needle, being in perfect equilibrium, can revolve
freely, or remain at reft, on the pivot, in whatever
iituation it may be placed. Before the magnet is ap-
P 2 plied.
212 ON THE MARINER S COMPASS*
plied, it would be proper to temper the needle, ill.
order to render it as hard as poffible ; then by rub-
bing or touching it with a good loadftone, it will in-
ftantly acquire the magnetic virtue. The two ex*
tremities will no longer balance each Other, but the
one D will defcend, as if it had become heavier ; and
in order to reftore the equilibrium, fomething mull
be taken away from the extremity B, or a fmall
weight added to the end A. But the artifts, fore-
feeing this change produced by magnetifm, make the
end B originally lighter than the end A, that the mag-
netized needle may of itfelf alfurne the horizontal
pofition.
It then acquires another property ftill much more
remarkable j it is no longer indifferent to all iitua-
tions, as formerly ; but affects one in preference to
every other, and difpofes itfelf in fuch a manner that
the extremity B is directed to the north nearly, and
the extremity A toward the fouth ; and the direction
of the magnetic needle correfponds almoft with the
meridian line.
You recollect that, in order to trace a meridian
line, which may point out the north and the fouth, it
is neceffary to have recourfe to aftronomical obfer-
vations, as the motion of the fun and ftars determines
that direction ; and when we are not provided with
the neceffary inftruments, and efpecially when the fky
is overclouded, it is impoffible to derive any affiftance
from the heavens toward tracing the meridian line ;
this property of the magnetic needle is, therefore, fo
much the more admirable, that it points out, at all
times,
ON THE MARINERS COMPASS. 213
times, and in every place, the northern direction, on
which depend the others, toward the eaft, fouth and
weft. For this reafon the ufe of the magnetic needle,
or compafs, is become univerfal.
It is in navigation that the advantages refulting
from the ufe of the compafs are moil confpicuous ;
it being always neceffary to direct the courfe of a
veffel toward a certain quarter of the world, in order
to reach a place propofed, conformably to geogra-
phic or marine charts, which indicate the direction
in which we ought to proceed. Before this difco-
very, accordingly, it was impoflible to undertake
long voyages ; the mariner durft not lofe light of the
coaft, for fear of miftaking his courfe, unkfs the Iky
was unclouded, and the liars pointed out the way.
A veffel on the wide ocean, without the know-
ledge of the proper courfe, would be precifely in the
ftate of a man who, with a bandage over his eyes,
was obliged to find his way to the great church of
Magdeburg ; imagining he was going one way, he
might be going another. The compafs, then, is the
principal guide in navigation, and it was not till after
this important difcovery that men ventured acrofs
the ocean, and attempted the difcovery of a new
world. What could a pilot do, without his compafs*
during or after a ftorm, when he could derive no
afliftance from the heavens ? Take whatever courfe
he might, he muft be ignorant in what direction he
was proceeding, north, fouth, or to any other quar-
ter. He would prefently deviate to fuch a degree,
as infallibly to lofe himfelf, But the compafs im-
. P 3 mediately
214 °N THE MARINER S COMPASS.
mediately puts him right 5 from which you will be
enabled to judge of the importance of the difcovery
of the magnetic needle, or mariner's compafs.
ttb Oftobet;, ij 6. 1.
LETTER LV.
Declination of the Compafs, arid Manner of obferving it*
THOUGH the magnetic needle affects the fitua-
tion of being directed from fouth to north,
there are accidental caufes capable of deranging this
direction, which mull be carefully avoided. Such
are the proximity of a loadftone, or of iron, or fteel.
You have only to prefent a knife to a magnetic
needle, and it will immediately quit it's natural di-
rection, and move toward the knife ; and, by draw-
ing the knife round the needle, you will make it af-
fume every pofiible direction. In order to be affured,
then, that the needle is in it's natural direction, you.
muft keep at a diltance from it all iron or fteel, as
well as magnets ; which is fo much the more eafy,
that thefe fubftances influence it's direction only when
very near it : once removed, their effect becomes
infenfible, unlefs in the cafe of a very powerful mag-
net, which might poffibly act on the needle at the
diftance of feveral feet.
But iron alone produces not this effect, as the com*
pafs may be ufed to advantage even in iron-mines.
You are perfectly fenfible, that under ground, in
mines, we are in the fame condition as at fea, when
the
•o-n'the mariner's compass. 215
the face of heaven is overclouded, and that it is ne-
ceffary to drive mines in a certain direction. Plans
are accordingly conftru&ed reprefenting all the tracks
hollowed out in the bowels of the earth, and this
operation is regulated merely by the compafs : this is
the object of the fcienee denominated fubterraneous
geometry.
To return to our compafs, or magnetic needle, I
have remarked that It's direction is only almoft
northerly ; it is therefore incorrect to fay that the
magnet has the property of always pointing nortk.
Having employed myfelf in the fabrication of many
magnetic needles, I ever found that their direction
at Berlin deviated about fifteen degrees from the
true meridian line ; now, an aberration of 1 50 is
very confidexable.
Figure 3, plate II. reprefents, firft, the true meri-
dian line drawn from north to fouth ; that which is
drawn at right angles with it indicates the eaft, to
the right hand ; and the weft, to the left. Now the
magnetic needle AB does not fall on the meridian,
but deviates from it an angle of 150, BO north.
This angle is denominated the declination, and fome-
v times the variation of the compafs or magnetic
needle : and as the extremity B, neareft the north,
deviates toward the weft, we fay, the declination is
? 50 wefterly.
Having thus determined the declination of the
magnetic needle, we can make it anfwer the fame
purpofe as if it pointed directly north. The needle
is ufually inclofed in a circle, and you have only to
P 4 mark
2l6 ON THE MARINER'S COMPASS.
mark on it the due north at the exact diftance from
the northern extremity of the needle, fo as to make
a declination of 1 50 weftward, and the line north-
fouth will indicate the true meridian line, and enable
us to afcertain the four cardinal points, north, eaft,
fouth and weft.
The better to difguife the fecret, the magnetic
needle is concealed in a circle of pafteboard, as re-
prefented in the figure, only the needle is rendered
invifible, the pafteboard covering it, and forming'
but one body with it, the centre of which is placed
on a pivot, in order to admit of a free revolution ;
it affumes of courfe a fituation fuch that the point
marked north is always directed to that point of the
horizon ; whereas the needle, which is not feen, in
effect deviates from it 1 50 to the weft. This con-
ftruction ferves only to difguife the declination, which
the vulgar confider as a defect, though it be rather
an object worthy of admiration, as we mall after-
wards fee ; and the pafteboard only increafing the
weight of the needle, prevents it's turning fo freely
as if it were unencumbered.
To remedy this, and more commodioufly to em-
ploy the compafs, the needle is depofited in a circu-
lar box, the circumference of which, divided into
3600, exhibits the name of the principal points of the
horizon. In the centre is the pivot or point which
fupports the needle, and this laft immediately' affumes
a certain direction ; the box is then turned till tfye
northern extremity of the needle B exactly corre-
fponds with the fifteenth degree on the circumfe-
rencej
ON THE MARINER'S COMPASS. 217
rence, reckoning from the north-weft ward; and then
the names marked will agree with the real quarters
of the world.
At fea, however, they employ needles cafed in
circles of pafteboard, the circumference of which is
divided into 360 degrees, to prevent the neceflityof
turning round the box ; then the pafteboard circle,
which is called the compafs, indicating the real quar-
ters of the world, we have only to refer to it the
courfe which the fhip is fleering, in order to afcer-
tain the direction, whether north or fouth, eaft or
weft, or any other intermediate point. By the com-
pafs likewife we diftinguifh the winds, or the quar-
ters from which they blow, and from the points
marked on it their names are impofed. It is necef-
fary, at any rate, to be perfectly allured of the de-
clination or variation of the compafs; we have found
it to be exactly 150 weft ward here at Berlin ; but it
may be different at other places, as I fhall afterwards
demonftrate.
IQtb OftobeT) 1 76 1.
LETTER LVI.
Difference in the Declination of the Compafs at the
fame Place.
WHEN I fay that the declination of the com-
pafs is 1 5 degrees weftward, this is to be
underftood as applying only to Berlin, and the pre-
sent time ; for it has been remarked, that not only
is
SlS ON THE MARINER'S COMPASS.
Is this declination different at different places of the
earth, but that it varies, with time, at the fame
place.
The magnetic declination is accordingly much
greater at Berlin now, than it was formerly. I re-
collect, the time perfectly when it was only i o° •> and
in the laft century there was a period, when there
was no declination, fo that the direction of the mag-
netic needle coincided exactly- with the meridian
line. This was about the year 1 670 ; fince then the
declination is become progreiTively greater toward
the weft, up to 1 50, as at this day : and there is
every appearance that it will go on diminifhing, till
It is again reduced to nothing. I give this, however,
merely as conjecture, for we are very far from being
able to predict it with certainty.
Befides, it is well known that prior to the year
1670, the declination was in the contrary direction,
that is, toward the eaft; and the farther back we go,
the greater do we find the declination eaftward.
Now, it is impoffible to go farther back than to the
period when the compafs was difcovered ; this hap-
pened in the fourteenth century ; but it was long
after the difcovery before they began to obferve the
declination at Berlin ; for it was not perceived at firft
that the needle deviated from the meridian line.
But at London, where this fubjecl: has been more
carefully ftudied, the magnetic declination, in the
year 1580, was obferved to be 1 1° i^ eaft ; in 1622,
6° o'eaft; in 1634, 40 5' eaft; in 1657 there was no
declination ; but in 1672 it was 20 30' weft; in 1692,
% 6° d
ON THE MARINER'S COMPASS. 219
6° o' weft ; and at prefent it may probably be 1 8 de-
grees weft or more. You fee then, that, about the
beginning of the laft century, the declination was
nearly 8 degrees eaft : that thenceforward it gradu-
ally diminifhed, till it became imperceptible in the
year 1657; and that fmce, it has become wefterly,
gradually increafmg up to the prefent time.
It has preferved nearly the fame order at Paris ;
but there it was reduced to nothing in 1 666, nine
years later than at London : hence you will obferve
a moft unaccountable diverfity of declination, rela-?
tively to different places of the earth, at the fame
time, and to the fame place, at different times.
At prefent, not only through all Europe, but
through all Africa, and the greateft part of Alia, the
declination is wefterly, in fome places greater, in
others lefs, than with us. It is greater in certain
countries of Europe than at our capital ; namely in
Scotland and in Norway, where the declination con-
siderably exceeds 200; in Spain, Italy, and Greece,
on the contrary, it is lefs, being about 1 1° ; on the
weftern coafts of Africa it is about io°, and on the
eaftern 1 20. But as you advance eaft ward into Afia
it progrefiively diminifhes, till it entirely difappears
in the heart of Siberia, at Jenifeifk ; it difappears too
in China, at Pekin, and at Japan ; but beyond thefe
regions, to the eaftward, the declination becomes
eafterly, and goes on increafmg in this direction,
along the north part of the Pacific Ocean, to the
weftern coafts of America, from which it proceeds
gradually diminishing, till it again difappears in Ca-
nada,
220 ON THE MARINERS COMPASS.
nada, Florida, the Antilles, and toward the coafts
of Brazil. Beyond thefe countries, toward the eaft,
that is, toward Europe and Africa, it again becomes
wefterly, as I have already remarked.
In order to attain a perfect knowledge of the pre-
fent ftate of magnetic declination, it would be ne-
ceffary to afcertain for all places, both ' at land and
fea, the prefent ftate of magnetic declination, and
whether it's tendency is weft ward or eaftward. This
knowledge would be undoubtedly extremely ufeful,
but we dare fcarcely hope for it. It would require
men of ability, in every part of the globe, employed,
at the fame time, in obferving, each on his own
flation, the magnetic declination, and who fhould
communicate their obfervations with the utmoft ex*
actnefs. But the fpace of fome years would elapfe
before the communications of the more remote could
be received ; thus the knowledge aimed at is unat-
tainable till after the expiration of years. Now,
though no very confiderable change takes place in
the direction of the magnetic needle in two or three
years, this change, however fmall, would however
prevent the attainment of complete information re-
specting the prefent ftate of the various declinations
of the magnetic needle, from obfervations made, at
the fame time, in the different regions of the globe.
The fame thing holds with refpecl to times paft ;
to every year correfponds a certain ftate of magnetic
declination proper to itfelf, and which diftinguifhes
it from every other period of time, paft and future.
.It were, however, iincerely to be wiihed, that we
had
ON THE MARINER S COMPASS; 221
had an exactly detailed ftate of the declination for
one year only ; the rhoft important elucidations of
the fubjed would certainly be derived from it.
The late Mr. Halky, a celebrated Englifh aftrono-
mer, has attempted to do this for the year 1700,
founding his conclufions on a great number of ob-
fervations made at different places, both by land and
fea ; but belide that fome very coniiderable diftricts,
where thefe obfervations were not made, are not
taken into his account, moft of thofe which he has
employed, were made feveral years prior to 1700;
fo that at this era the declination might have under-
gone very coniiderable alterations. It follows, that
this ftatement, which we find reprefented on a ge-
neral chart of the earth, mull be conlidered as ex-
tremely defective ; and, moreover, what would it
now avail us to know the ftate of magnetic declina-
tion for the year 1700, having fince then undergone
a coniiderable change ?
Other Englifh geographers have produced, pofte-
rior to that period, a limilar chart, intended to re-
prefent all the declinations, fuch as they were in the
year 1 744. But as it has the fame defect with that of
Mr. Halley ; and as they likewife were unable to pro-
cure obfervations from feveral countries on the globe9
they did not fcruple to fill up the vacant places, by
confulting Halley's chart, which certainly could not
apply to 1 744. You will conclude, from what I have
faid, that our knowledge of this important branch
of phyfics is ftill extremely imperfect.
i$tb Oflober, 1761.
LETTER
222 ON THE MARINER S COMPASS;
LETTER LVII.
Chart of Declinations ; Method of employing it for the
Difcovery of the Longitude.
T may be proper, likewife, to explain in what
manner Halley proceeded to reprefent the mag-
netic declinations, in the chart which he conftructed
for the year 1700, that if you mould happen to fee
it, you may comprehend it's ftructure.
Firft, he marked, at every place, the declination
of the magnetic needle, fuch as it had been there ob-
ferved. He diftinguifhed, among all thefe places,
thofe where there was no declination, and found
that they all fall in a certain line, which he calls the
line of no declination, as every where under that
line there was then none. This line was neither a
meridian nor a parallel, but run in a very oblique
direction over North America, and left It near the
coafts of Carolina ; thence it bent it's courfe acrofs
the Atlantic Ocean between Africa and America*
Befide this line he difcovered likewife another, in
which the declination difappeared; it defcended
through the middle of China, and palled from thence
through the Philippine Ifles and New Holland. It is
eafy to judge, from the track of thefe two lines, that
they have a communication near both poles of the
s;lobe.
Having fixed thefe two lines of nO declination,
Mr. Halley remarked that, every where between the
fir/'.:
ON THE MARINER'S COMPASS. 223
firft and laft, proceeding from weft to eaft, that is
through all Europe, Africa, and almoft the whole of
Afia, the declination was wefterly 5 and that on the
other fide, between thofe lines, that is„ over the
whole Pacific Ocean, it was eafterly. After this, he
obferved all the places in which the declination was
5 degrees weft, and found he could ftill conveniently
draw a line through all thefe places, which he calls
the line of five degrees weft. He found likewife two
lines of this defcription, the one of which accompa-
nied, as it were, the firft of no declination, and the'
other the laft. He went on in the fame manner with
the places where the declination was io°; afterwards
1 <j°, 200, &c. and he faw that thefe lines of great de-
clination were confined to the polar regions ; whereas
thofe of fmall declination encompafied the whole
globe, and palled through the equator.
In fact, the declination fcarcely ever exceeds 150
©n the equator, whether weft or eaft ; but on ap-
proaching the poles, it is pofiible to arrive at places*
where the declination exceeds 5 8° and 6o°. There
are undoubtedly fome, where it is ftill greater, ex*
ceeding even 908, and where the northern extremity
of the needle will confequently turn about and point
fouthward.
Finally, having drawn flmilar lines through the
places where the declination was eaftward io°, 15°^
20 °, and fo on, Mr. Ha Iky filled up the whole chart*
which reprefented the entire furface of the earth*
under each of which lines the declination is univer-
&lly the lame,, provided the obfervations are not er-
rcneous.
224 oN THE mariner's compass.
roneous. Mr. Halley has, accordingly, fcrupuloufly
abftained from continuing fuch lines beyond the"
places where obfervations had actually been made %
for this reafon the greater part of his chart is a
blank.
Had we fuch a chart, accurate and complete, we
fhould fee, at a glance, what declination mull have
predominated at each place, at the time for which
the chart was conftructed ; and though the place, in
queftion, fhould not be found precifely under one of
the lines traced on the chart, by comparing it with
the two lines between which it might be fituated,
we could eafily calculate the intermediate declination
which correfponded to it. If I found my prefent
place to be between the lines of i o° and 1 50 of weft-
ern declination, I fhould be certain that the declina-
tion there was more than 1 o°, and lefs than 1 50 ;
and according as I might be nearer the one or the
other, I could eafily find the juft medium, which
would indicate the true declination.
From this you will readily comprehend, that if
we had fuch a chart, thus exact, it would aflift us in
difcovering longitude, at leaft for the time to which
it correfponded. In order to explain this method,
let us fuppofe that we are pofieffed of a chart con-
ftrucled for the prefent year, we would fee on it,
firft, the two lines drawn through the places where
there is no declination ; then the two where it is 50,
io°, 1 50, 200, both eaft and weft : let us farther fup-
pofe that, for the greater exactnefs, thefe lines were
drawn from degree to degree, and that I found my-
felf
on The mariner's compass. 225
felf at a certain place on fea, or in an unknown
country, I would in the firft place draw a meridian
line, in order to afcertain how much my compafs
deviated from it, and I mould find, for example,
that the declination is precifely 1 o° eafl ; I mould
then take my chart, and look for the two lines under
which the declination is 1 o° eafl, fully affured that
1 am under the one or the other of thefe two lines,
which muft at once greatly relieve my uncertainty.
Finally, I would obferve the height of the pole,
which being the latitude of my place, nothing more
would remain but to mark, on the two lines men-
tioned, the points where the latitude is the fame with
that which I have juft obferved ; and then all my
uncertainty is reduced to two points very diflant
from each other ; now, the circumftances of my
voyage would eafily determine which of thofe two
places is that where I actually am.
You will admit that if we had charts fuch as I have
defcribed, this method would be the moft commo-
dious and accurate of all, for afcertainino; the lonori-
tude : but this is precifely the thing we want ; and
as we are ftill very far from having it in our power
to conftruct. one for the time paft, which would be
of no ufe for the prefent time, for want of a fuffi-
cient number of obfervations, we are ftill lefs in-<
ftructed refpecting all the changes of declination
which every place undergoes in the lapfe of time.
The obfervations hitherto made afrure us, that cer-
tain places are fubjecl: to very conliderable variations,
and that others fcarcely undergo any, in the fame
Vol. II. Q inter va]
226 ON THE MAGNETIC NEEDLE.
interval of time ; which ftrips us of all hope of ever
being able to profit by this method, however excel-
lent it may be in itfelf.
\yth Ottober, 1761.
LETTER LVIII.
Why does the Magnetic Needle affecl, in every Place of
the Earth, a certain Direclion, differing in different
Places ; and for what Reafon does it change, with
Time, at the fame Place ?
YOU will undoubtedly have the curiofity to
be informed, why magnetic needles affecl;, at
every place on the globe, a certain direction ; why
this direction is not the fame at different places ; and
why, at the fame place, it changes with the courfe
of time ? I fhall anfwer thefe important enquiries to
the beft of my ability, though I fear not fo much
to your fatisfaction as I could wifh.
I remark, firft, that magnetic needles have this
property in common with all magnets, and that it is
only their form, contrived to balance and revolve
freely on a pivot, which renders it more confpicuous.
The loadftone, fufpended by a thread, turns toward
a certain quarter, and when put in a fmall veffel to
make it fwim on water, the veffel which fupports
the loadftone will always affect a certain direclion.
Every loadftone fitted with two oppofite points, the
one of which is directed to the north, and the other
to
ON THE MAGNETIC NEEDLE. 227
to the fouth, will be fubjed to the fame variations
e magnetic needles.
Thefe points are very remarkable in all loadftones,
as by them iron is attracted with the greateft force.
They are denominated the poles of a loadftone, a
term borrowed from that of the poles of the earth
or of the heavens j becaufe the one has a tendency
toward the north and the other toward the fouth
pole of the earth ; but this is to be underftood ass
only almoft, not exactly, the cafe; for when the
name was impofed, the declination had not yet been
obferved. That pole of the loadftone which is di-
rected northward is called it's north pole, and that
which points fouthward it's fouth pole.
I have already remarked, that a magnetic needle,
as well as the loadftone itfelf, amimes this fttuation,
which appears natural to it, only when removed from
the vicinity of another loadftone, or of iron. When.
a magnetic needle is placed near a loadftone, it's fitua-
tion is regulated by the poles of that loadftone ;
fo that the north pole of the loadftone attracts the
fouthern extremity of the needle?i and "reciprocally
the fouth pole of the loadftone the northern extre-
mity of the needle. For this reafon, in referring
one loadftone to another, we call thofe the friendly
poles which bear different names, and thofe the
hoftile which have the fame name. This property
is fingularly remarkable on bringing two loadftones
near each other : for then, we find that not only do
the poles of different names mutually attract, but
that thofe of the fame name fhun and repel each
O 2 other.
S2S ON THE MAGNETIC NEEDLE.
other. This is ftill more confpicuous when two
magnetic needles are brought within the fphere of
mutual influence.
In order to be fenfible of this, it is of much im-
portance to conlider the fituation which a magnetic
needle affumes in the vicinity of a loadftone.
The bar AB, (plate II. Jig. 4. J reprefents a load-
ftone, whofe north pole is B, and the fouth pole A :
you fee various positions of the magnetic needle, un-
der the figure of an arrow, whofe extremity marked
b is the north pole, and a, the fouth. In all thefe
portions, the extremity b of the needle is dire&ed
toward the pole A of the loadftone ; and the extre-
mity a to the pole B. The point c indicates the
pivot on which the needle revolves ; and you have
only to conlider the figure with fome attention, in
order to determine what fituation the needle 'will
affume, in whatever pofition round the loadftone
the pivot c is fixed.
If there were, therefore, any where, a very large
loadftone AB, the magnetic needles placed round it
would affume, at every place, a certain fituation, as
we fee aclually to be the cafe round the globe. Now
if the globe itfelf were that loadftone, we fhould'
comprehend why the magnetic needles every where
affumed a certain direction. Naturalifts, accordingly,
in order to explain this phenomenon, maintain that
the whole globe has the- property of a magnet, or
that we ought to confider it as a prodigious load-
ftone. Some of them allege, that there is at the
centre of the earth a very large loadftone, which has
exercifed
ON THE MAGNETIC NEEDLE. 2ZQ
exercifed it's influence on all the magnetic needles,
and even on all the loadftones, which are to be found
on the furface of the earth ; and that it is this in-
fluence which directs them in every place, conform-
ably to the directions which we obferve them to
aflume.
But there is no occafion to have recourfe to a
loadftone concealed in the bowels of the earth. It's
furface is fo replenished with mines of iron and load-
ftone, that their united force may well fupply the
want of this huge magnet. In fact, all loadftones
are extracted from mines, an infallible proof that
thefe fubftances are found in great abundance in the
bowels of the earth, and that the union of all their
powers furnifhes the general force, which produces
all the magnetical phenomena. We are like wife en-
abled thereby to explain, wherefore the magnetic
declination changes, with time, at the fame place ;
for [it is well known, that mines of every kind of
metal are fubject to perpetual change, and particu-
larly thofe of iron, to which the loadftone is to be
referred. Sometimes iron is generated, and is fome-
times deftroyed at one and the fame place ; there are
accordingly, at this day, mines of iron where there
were none formerly ; and where it was formerly
found in great abundance, there are now hardly any
traces of it. This is a fufficient proof, that the total
mafs of loadftones contained in the earth is under-
going very confiderable changes, .and thereby, un-
doubtedly, the poles, by which the magnetic decil-
es 3 nation
230 ON THE MAGNETIC NEEDLE,
nation is regulated, iikewife change with the lapfe of
time. .
Here then we muft look for the reafon, why the
magnetic declination is fubject to changes fo confi-
derable at the fame places of the globe. But this
very reafon, founded on the inconftancy of what is
palling in it's bowels, affords no hope of our ever
being able to afcertain the magnetic declination be-
forehand, uniefs we could find the means of fubject-
ing the changes of the earth to fome fixed law. A
long feries of obfervations, carried on through feve-
ral ages fuccefiively, might poflibly throw fome light
on the fubjecL
20/£ Oflober, 1 76 1.
LETTER LIX.
Elucidations refpecling the Caufe and Variation of the.
Declination of Magnetic Needles.
r 1 "'HOSE who allege that the earth contains in it's
.-*- womb a prodigious loadftone, like a ftone with
a kernel in fruit, are under the necefiity of admit-
ting, in order to explain the magnetic declination,
that this ftone is fuccefiively fhifting it's fituation.
It muft in that cafe be detached from the earth in all
it's parts ; and as it's motion would undoubtedly
follow a certain law, we might flatter ourfelves with
the hope of one day difcovering it. But whether
there be fuch a magnetic ftone within the earth,
or
ON THE MAGNETIC NEEDLE, 23*
or whether the loadftones fcattered up and down
through it's entrails unite their force to produce the
magnetical phenomena, we may always confider the
earth itfelf as a loadftone, in fubferviency to which
every particular loadftone, and all magnetic needles,
affume their direction.
Certain naturalifts have enclofed a very powerful
magnet in a globe, and having placed a magnetic
needle on it's furface, obferved phenomena fimilar to
thofe which take place on the globe of the earth, by
placing the magnet within the globe, in feveral dif-
ferent pofitions. Now, confidering the earth as a
loadftone, it will have it's magnetic poles, which mull
be carefully diftingurfhed from the natural poles,
round which it revolves. Thefe poles have nothing
in common between them but the name ; but it is
from the pofition of the magnetic poles, relatively
to the natural, that the apparent irregularities in the
magnetic declination proceed, and particularly of the
lines traced on the globe, of which I have endea-
voured to give you fome account.
In order more clearly to elucidate this, fubjecl, I
remark, that if the magnetic poles exactly coincided
with the natural, there would be no declination all
over the earth : magnetic needles would univerfally
point to the north precifely, and their pofition would
be exactly that of the meridian line. This were no
doubt an unfpeakable advantage in navigation, as
we mould then know with precifion the courfe of
the veflel and the direction of the wind j whereas,
at prefent, we muft always look for the declination
Q4 of
232 ON THE MAGNETIC NEEDLE.
of the compafs before we are able to determine the
true quarters of the world. But then the compafs
could furnim no affiftance toward afcertaining the
longitude, an object, which the declination may fooner
or later render attainable.
Hence it may be concluded, that if the magnetic
poles of the earth differed very greatly from the na-
tural, and that if they were directly oppofite to each
other, which would be the cafe, if the magnetic axis
of the earth, that is the ftraight line drawn from the
one magnetic pole to the other, paifed through the
centre of the earth, then magnetic needles would
univerfally point toward thefe magnetic poles, and
it would be eafy to affign the magnetic direction
proper to every place ; we mould only have to draw
for every place a circle which mould at the fame time
pafs through the two magnetic poles, and the angle
which this circle would make with the meridian of
the fame place muft give the magnetic declination.
In this cafe, the two lines, under which there is no
declination, would be the meridians drawn through
the magnetic poles. But as we have feen that, in
reality, thefe two lines without declination are not
meridians, but take a very unaccountable direction,
it is evident that no fuch cafe actually takes place.
Halley clearly faw this difficulty, and therefore thought
himfelf obliged to fuppofe a double loadftone in the
bowels of the earth, the one fixed, the other move-
able ; of confequence, he was obliged to admit four
poles of the earth, two of them toward the north,
and two toward the fouth, at unequal diftances.
But
ON THE MAGNETIC NEEDLE, 233
But this hypothefis feems to me rather a bold con-
jecture : it by no means follows, that becaufe thefe
lines of no declination are not meridians, there muft
be four magnetic poles on the earth : but rather,
that there are only two, which are not directly op-
pofite to each other j or, which comes to the fame
thing, that the magnetic axis does not pafs through
the centre of jthe earth.
It remains, therefore, that we confider the cafes in
which thefe two magnetic poles are not directly op-
polite, and in which the magnetic axis does not pafs
through the centre of the earth ; for if we embrace
the hypothefis of the magnetic nut within the earth,
why mould one of it's poles be precifely oppofite to
the other ? This nut may very probably be not ex-
actly in the very centre of the earth, but at a confi-
derable diftance from it. Now, if the magnetic poles
are not diametrically oppofite to each other, the lines
of no declination may actually afiume a direction
limilar to that which, from obfervation,we find they
do ; it is even poflible to affign to the two magnetic
poles fuch places on the earth, that not only thefe
lines mould coincide with obfervation, but likewife,
for every degree of declination, whether weftern or
eaftern, we may find lines ^precifely fimilar to thofe
which, at firlt, feemed fo unaccountable.
In order, then, to know the ftate of magnetic de-
clination, all that is requifite, is to fix the two mag-
netic poles ; and then it becomes a problem in geo-
metry, to determine the direction of all the lines
which I mentioned in my preceding letter, drawn
for
234 PN THE MAGNETIC NEEDLE.
for every place where the declination is the fame 5
by fuch means too we fhould be enabled to rectify
thefe lines, and to fill up the countries where no ob»
fervations have been made: and were it poflible to
aflign, for every future period, the places of the two
magnetic poles on the globe, it would undoubtedly
prove the inoft fatisfying folution of the problem of
the longitude.
There is no occafion, therefore, for a double load-
ftone within the earth, or for four magnetic poles, in
order to explain the declination of magnetic needles,
as Hailey fuppofed, but for a fimple magnet, or two
magnetic poles, provided it's juft place is affigned to
each. It appears to me that, from this reflection^
we are much more advanced in our knowledge of
magnetifm.
Z^tb 0 Sober 1 1761.
LETTER LX.
Inclination of Magnetic Needle*.
r OU will pleafe to recoiled, that on rubbing a
needle againft the loadftone it acquires not
only the property of pointing toward a certain point
of the horizon, but that it's northern extremity links,
as if it had become heavier, which obliges us to di-
minish it's weight fomewhat, or to increafe that of
the other extremity, in order to reftore the equili-
brium. 1 have, without putting this in practice,
made feveral experiments to afcertain how far the
magnetic
ON THE MAGNETIC NEEDLE. 235
magnetic force brought down the northern extre-
mity of the magnetized needle, and I have found
that it funk fo as to, make an angle of 72 degrees
with the horizon, and that in this fituation the needle
remained at reft. It is proper to remark, that thefe
experiments were made at Berlin, about fix years
ago ; for I fhall ihew you afterwards, that this di-
rection to below the horizon, is as variable as the
magnetic declination.
Hence we fee that the magnetic power produces a
double effect on needles ; the one directs the needle
toward a certain quarter of the horizon, the devia-
tion of which from the meridian line is what we call
the magnetic declination ; the other impreffes on it
an inclination toward the horizon, finking the one
or the other extremity under it, up to a certain
angle.
Let d e (plate II. fig, 5. J be the horizontal line,
drawn according to the magnetic declination, and
the needle will affume, at Berlin, the fituation b as
which makes with the horizon d e the angle deb
or e c a9 which is 72°, and confequently, with the
vertical fg, an angle beg or acfoi 18 degrees.
This fecond effect of the magnetic force, by which the
magnetic needle affects a certain inclination toward
the horizon, is as remarkable as the firft ; and as the
fir ft is denominated the magnetic declination , the fe-
cond is known by the name of magnetic inclination ,
which deferves, as well as the declination, to be every
where obferved with all pofiible care, as we find in
it a fimilar variety.
3 The
2$6 ON THE MAGNETIC NEEDLE.
The inclination at Berlin has been found 720, at
Bale only 700, the northern extremity of the needle
being funk, and the oppofite, of confequence, raifed
to that angle. This takes place in countries which
are nearer to the northern magnetic pole of the
earth ; and in proportion as we approach it, the
greater becomes the inclination of the magnetic
needle, or the more it approaches the vertical line ;
fo that if we could reach the pole itfelf, the needle
would there actually affume a vertical fituation, it's
northern extremity pointing perpendicularly down-
ward, and its fouthern end upward. The farther,
on the contrary, you remove from the northern mag-
netic pole of the earth, and approach the fouthern,
the more the inclination diminifhes ; it will at length
difappear, and the needle will affume a horizontal
pofition, when equally diftant from both poles : but
in proceeding toward the fouth pole of the earth,
the fouthern extremity of the needle will fink more
and more under the horizon, the northern extre-
mity riling in proportion, till at the pole itfelf, the
needle again becomes vertical, with the fouthern ex-
tremity perpendicularly downward, and the northern
upward.
It were devoutly to be wifhed that experiments
had been as carefully, and as generally made, in the
view of afcertaining the magnetic inclination, as of
determining the declination ; but this important ar-
ticle of experimental philofophy has hitherto been
too much neglected, though certainly neither lefs
curious, nor lefs interefting, than that of the declina-
tion.
ON THE MAGNETIC NEEDLE* Itf
tion. It is not however a matter of furprize ; expe-
riments of this fort are fubject to too many difficul-
ties ; and almoft all the methods hitherto attempted
of obferving the magnetic inclination have failed.
One artift alone, Mr» Diterich of Bale^ has fucceeded*
having actually conftructed a machine proper for the
purpofe, under the direction of the celebrated Mr,
Daniel BernoiillU. He fent me two Of thefe machines i
by means of which I have obferved, at Berlin, this
inclination of 72 degrees ; and however curious, in
other refpects, the Englifh and French may be, in
profecuting fuch enquiries, they have put no great
value on Mr. Diterich's machine, though the only
one adapted to the defign. This inftance demon-
ftrates how the progrefs of fcience may be obftructed
by prejudice j hence Berlin and Bale are the only
two places on the globe, where the magnetic inclina-
tion is known.
Needles prepared for the conftruction of compaffes
are by no means proper to indicate the quantity of
magnetic inclination, though they may convey^ a
rough idea of it's effect, becaufe the northern extre-
mity in thefe latitudes becomes heavier. In order
to render ferviceable needles intended to difcover the
declination, we are under the neceffity of defer oying
the effect of the inclination, by diminifhing the
weight of the northern extremity, or increafing that
of the fouthern. To reitore the needle to a hori-
zontal polkion, the laft of thefe methods is uiually
employed, and a fmall morfel of wax is affixed to
' the fouthern extremity of the needle. You are abun-
dantly
238 ON THE MAGNETIC NEEDLE.
dantly fenfible, that this remedy applies only to thefe
regions of the globe, where the inclinatory power is
fo much, and no more ; and that were we to travel5
with fuch a needle, toward the northern magnetic
pole of the earth, the inclinatory power would in-
creafe, fo that to prevent the effect we (hdillct be
obliged to increafe the quantity of wax at the fouth=
ern extremity. But were we travelling fouthward,
and approaching the oppofite pole of the earth, where
the inclinatory power on the northern extremity of
the needle diminifhes, the quantity of wax affixed
to the other extremity muft then likewife be dimi-
nifhed ; after that it muft be taken away altogether;
being wholly ufelefs when we arrive at places where
the magnetic inclination difappears. On proceeding
ftill forward to the fouth pole, the fouthern extre-
mity of the needle links ; fo that to remedy this, a
morfel of wax muft be affixed to the northern ex-
tremity of the needle. Such are the means employed;
in long voyages, to preferve the compafs in a hori-
zontal pofition.
In order to obferve the magnetic inclination, it
would be neceffary to have inftruments made on pur-
pofe, fimilar to that invented by the artift of Bale*
His inftrument is called the inclinatory, but there is
little appearance of it's coming into general ufe.* It
* Since this was written, on occafion of the late tranfit of Venus
over the fun's dilk, Meffrs, Mallet and Piclet of Geneva, employed
to obferve that trantit in Lapland, made ufe of the inclinatory, and
found, in the month of May, 1769, the magnetic inclination firft
atPeterfburg to be 73°4o'; afterwards at Kola in Lapland 770 45';
at Oumba 750 10'; and at Panoi 760 30',
is
MAGNETIC DIRECTION. 1^
is fill! lefs to be expected that we mould foon have
charts conftructed on the magnetic inclination, fimi-
lar to thofe which reprefent the declination. The
fame method might eafily be followed, by drawing
lines through all the places where the magnetic in-
clination is the fame : fo that we fliould have lines
at no inclination ; afterwards other lines where the
inclination would be 50, io°, 15°, 2o(
whether northward or fouthward.
27 tb O&ober, 1761.
LETTER LXI.
True Magnetic Direclion ; filbtile Matter which produces
the Magnetic Power.
TN order to form a juft idea of the effect of the
■*■ earth's magnetic power, we muft attend at once
to the declination and inclination of the magnetic
needle, at every place of the globe. At Berlin, we
know, the declination is 150 weft, and the inclina-
tion of the northern extremity 7 2°. On confider-
ing this double effect, the declination and inclina-
tion, we fhall have the true magnetic direction for
Berlin. We draw-firft, on a horizontal plane, a line
which fhall make with the meridian an angle of 150
weft, and thence, descending toward the vertical line,
we trace a new line which fhall make with it an
angle of 720; and this will give us the magnetic di-
rection for Berlin ; from which you will compre-
hend, how the magnetic direction for every other
place
4«3 MAGNETIC POWER*
place is to be afcertained, provided the inclination
and declination are known*
Every magnet exhibits phenomena altogether
fimilar. You have only to place one on a table co-
vered with filings of fteel, and you will fee the filings
arrange themfelves round the loadftone AB, nearly
as reprefented in fig. 6, plate II. in which every par-
ticle of the filings may be confidered as a fmall mag-
netic needle, indicating, at every point round the
loadftone, the magnetic direction. This experiment
leads to inquire into the caufe of all thefe pheno-
mena.
The arrangement afhimed fey the fleel filings leaves
no room to doubt that it is a fubtile and invifible
matter which runs through the particles of the fleel,
and difpofes them in the direction which we here
obferve. It is equally clear that this fubtile matter
pervades the loadftone itfelf, entering at one of the
poles, and going out at the other : fo as to form, by
it's continual motion round the loadftone, a vortex
which re-conducts the fubtile matter from one pole
to the other, and this motion is, without doubt, ex-
tremely rapid.
The nature of the loadftone confifts, then, in a con-
tinual vortex, which diftinguifhes it from all other
bodies ; and the earth itfelf, in quality of loadftone,
muft be furrounded with a fimilar vortex, acting
every where on magnetic needles, and making con-
tinual efforts to difpofe them according to its own
direction, which is the fame I formerly denominated
the magnetic direction : this fubtile matter is conti-
nually
MAGNETIC POWER. 24I
nually iffuing, then, at one of the magnetic poles of
the earth, and after having performed a circuit round
to the other pole, it there enters, and pervades the
globe through and through to the oppofite pole,
where it again efcapes.
We are not yet enabled to determine by which of
the two magnetic poles of the earth it enters or
iffues : the phenomena depending on this have fach
a perfect refemblance, that they are indiilinguimable.
It is undoubtedly, likewife, this general vortex of
the globe which fupplies the fubtile matter of every
- particular loadftone to magnetic iron or fteel, and
which keeps up the particular vortices that furround
them.
In order to a thorough inveftigation of the nature
of this fubtile matter, and it's motion, it muft be re-
marked, that it's action is confined to loadftone, iron
and fteel ; all other bodies are abfolutely indifferent
to it ; the relation which it bears to thofe muft,
therefore, be by no means the fame which it bears
to others. We are warranted to maintain, from
manifold experiments, that this fubtile matter freely
pervades all other bodies, and even in all directions :
for, when a loadftone acts on a needle, the action is
perfectly the fame whether another body interpofes
or not, provided the interpofing body is not iron,
and it's action is the fame on the filings of iron.
This fubtile matter, therefore, muft pervade all bor
dies, iron excepted, as freely as it does air, and even
pure ether ; for thefe experiments facceed equally
well in a receiver exhaufted by the air-pump. This
Vol. II. R _ matter
242 MAGNETIC POWER.
matter is confequently different from ether, and even
much more fubtile. And, on account of the general
vortex of the earth, it may be affirmed that 'the globe
is completely furrounded by it, and freely pervaded,
as all other bodies are, excepting the loadftone and
iron : for this reafon, iron and fteel may be deno-
minated magnetic bodies, to diftinguifh them from
others.
But if this magnetic matter paffes freely through
all non-magnetic bodies, what relation can it have to
thofe which are fuch ? We have juft obferved that
the magnetic vortex enters at one of the poles of
every loadftone, and goes out at the other ; whence
it may be concluded, that it freely pervades load-
ftones likewife ; which would not diftinguifh them
from other bodies. But as the magnetic matter
paffes through the loadftone only from pole to pole,
this is a circumftance very different from what takes
place in others. Here, then, we have the diftinctive
character. Non-magnetic bodies are freely pervaded
by the magnetic matter, in all directions : loadftones
are pervaded by it, in one dire&ron only ; one of
the poles being adapted to it's admiffion, the other
to it's efcape. ~ But iron and fteel, when rendered
magnetic, fulfil this laft condition ; when they are
not, it may be affirmed, that they do not grant a
free tranfmiffion to the magnetic matter, in any di-
rection.
This may appear ftrange, as iron has open pores,
which tranfmit the ether, though it is not fo fubtile"
as the magnetic matter. But we muft carefully dif-
tinguifh
NATURE OF MAGNETIC MATTER. 243
tingulfh a iimple paflage, from one in which the
magnetic matter may pervade the body, with all it's
rapidity, without encountering any obftacle.
yfi Qflober, 1761.
LETTER LXII.
Nature of the Magnetic Matter, a?id of it's rapid
Current. Magnetic Canals.
AM very far from pretending to explain per-
fectly the phenomena of magnetiim ; it prefents
difficulties which I did not find in thofe of electricity.
The caufe of it undoubtedly is, that electricity con-
lifts in a too great, or too fmall, degree of compref-
iion, of a fubtile fluid which occupies the pores of
bodies, without fuppoiing that fubtile fluid, which is
the ether, to be in actual motion ; but magnetifm
cannot be explained, unlefs we fuppofe a vortex in
rapid agitation, which penetrates magnetic bodies.
The matter which conftitutes thefe vortices is
likewife much more fubtile than ether, and freely
pervades the pores of loadftones, which are imper-
vious even to ether. Now, this magnetic matter is
diffufed through, and mixed with, the ether, as the
ether is with grofs air, or juft as ether occupies and
fills up the pores of air, it may be affirmed that the'
magnetic matter occupies and fills the pores of ether.
I conceive, then, that loadftone and iron have
pores fo fmall that the ether in a body connot force
it's way into them, and that the magnetic matter
R 2 alone
244 NATURE OF MAGNETIC MATTER.
alone can penetrate them ; and which, on being ad-
mitted, Separates itfelf from the ether, by what may
be called a kind of filtration. In the pores of the
loadftone alone, therefore, is the magnetic matter to
be found in perfect purity : every where elfe it is
blended with ether, as this laft is with the air.
You can eafily imagine a feries of fluids, one al-
ways more fubtile than another, and which are per-
fectly blended together. Nature furnifhes inflances
of this. Water, we know, contains in it's pores par-
ticles of air, which are frequently feen difcharging
themfeives in the form of fmall bubbles : air again,
it is equally certain, contains in it's pores a fluid in-
comparably more fubtile, namely ether, and which,
on many occafions, is feparated from it, as in elec-
tricity. And now we fee a ftill farther progreffion,
and that ether contains a matter much more fubtile
than itfelf, the magnetic matter, which may, per-
haps, contain, in it's turn, others ftill more fubtile, at.
leaft this is not impoflible.
Having fettled this magnetic matter, let us fee how
it's phenomena are produced. I confider a loadftone,
then, and fay, firft, that befides a great many pores
filled with ether, like all other bodies, it contains
fome ftill much more narrow, into which the mag-
netic matter alone can find admiflion. Secondly,
thefe pores are difpofed in fuch a manner as to have
a communication with each other, and conftitute
tubes or canals, through which the magnetic matter
pafles from the one extremity to the other. Finally,
this matter can be transmitted through thefe tubes
only
NATURE OF MAGNETIC MATTER. 245
only in one direction, without the pofibility of re-
turning in an oppofite direction. This mod effential
circumftance requires a more particular elucidation.
Firft, then, I remark, that the veins and lymphatic
veffels in the bodies of animals, are tubes of a limilar
conftruction, containing valves, reprefented injtg. 7,
plate II. by the ftrokes m n9 whofe office it is to grant,
by railing themfelves, a free paffage to the blood when
it flows from A to B, and to prevent it's reflux from
B to A. For if the blood attempted to flow from B
to A, it would prefs down the moveable extremity of
the valve m on the fide of the vein 0, and totally ob-
ftruct the paffage. Valves are thus employed in aque-
ducts, to prevent the reflux of the water. I do not
confider myfelf, then, as fuppoflng anything contrary
to nature, when I fay, that the canals, in loadflones,
which admit the magnetic matter only, are of the
fame conftruction.
Figure 8, plate II. reprefents this magnetic canal,
according to my idea of it. I conceive it furnilhed
inwardly with briftles directed from A toward B,
which prefent no oppofition to the magnetic matter
in it's paffage from A to B, for in this cafe they open
of themfelves at n, to let the matter pafs at 0 ; but
they would immediately obftrucl the channel, were
it to attempt a retrograde courfe from B to A. The
nature of magnetic canals confifts, then, in granting
admiflion to the magnetic matter only at A, to flow
toward B, without the poflibility of returning in the
oppofite direclion from B toward A.
R 3 This
246 NATURE OF MAGNETIC MATTER.
This conftruction enables us to explain how the
magnetic matter enters into thefe tubes, and flies
through them with the greateft rapidity, even when
the whole ether is in a ftate of perfect reft, which is
the moft furprifmg : for how can a motion fo rapid
be produced ? This will appear perfectly clear to you,
if you will pleafe to recollect < that ether is a matter
extremely elaftic; accordingly the magnetic matter,
which is fcattered about, will be preffed by it on
every fide. Let us fuppofe the magnetic canal A B
ftill quite empty, and that a particle of magnetic
matter m prefents itfelf at the entrance A, and this
particle preffed on every fide at the opening of the
canal, into which the ether cannot force admiffion, it
will there be preffed forward with prodigious force,
and enter into the canal with equal rapidity ; another
particle of magnetic matter will immediately prefent
itfelf, and be driven forward with the fame force,
and in like manner all the following particles. There
will thence refult a continual flux of magnetic mat-
ter, which, meeting with no obftruftion in this canal,
will efcape from it at B, with the fame rapidity that
it enters at A.
My idea, then, is, that every loadftone contains a
great multitude of thefe canals, which I denominate
magnetic ; and it very naturally follows, that the
magnetic matter difperfed in the ether- muft enter
into them at one extremity, and efcape at the other,
with great impetuofity ; that is, we fhall have a per-
petual current of magnetic matter through the canals
of
Vri.jr.
.PUcle.ir.
*&$JgS£L
-A-
B
0
VI 0
n ' o
*<■■■■
n o
rx 0
ACTION OF MAGNETS. 247
of the loadftone : and thus I hope I have furmounted
the greateft difficulties which can occur in the theory
of maoTietifm.
o
3 d November, I jr 6 r .
LETTER LXIII.
Magnetic Vortex. Aclion of Magnets upon each other.
Y
OU have now feen in what the diftinctive cha-
racter of the loadftone con lifts ; and that each
contains feveral canals, of which I have attempted a
defcription.
Figure 1. plate III. reprefents a loadftone A B, with
three magnetic canals a b, through which the mag-
netic matter will flow with the utmoft rapidity, en-
tering at the extremities marked a, and efcaping at
thofe marked b : it will eicape indeed with the fame
rapidity, but immediately meeting with the ether
blended with the groffer air, great obftructions will
oppofe the continuation of it's motion in the fame
direction ; and not only will the motion be retarded,
but it's direction diverted toward the fides c c. The
fame thing will take place at the entrance, toward
the extremities a a a; on account of the rapidity
with which the particles of magnetic matter force
their way into them, the circulation will quickly
overtake thofe which are ftill toward the fides e e,
and thefe, in their turn, will be replaced by thofe
which, efcaped from the extremities b b b, have been
already diverted toward c c ; fo that the fame mag-
R 4 netic
248 ACTION OF MAGNETS
netic matter which iflued from the extremities b b b
quickly returns toward thofe marked a a a, perform-
ing the circuit b c d e a, and this circulation, round
the loadftone, is what we call the magnetic vortex.
It muft not be imagined, however, that it is al-
ways the fame magnetic matter, which forms thefe
vortices ; a confiderable part of it will efcape, no
doubt, as well toward B as toward the fides, in per-
forming the circuit ; but as a compenfation,. frefh
magnetic matter will enter by the extremities a a a,
fc that the matter which conftitutes the vortex is
fuccedaneous and very variable : a magnetic vortex,
furrounding the loadftone, will, however, always be
kept up, and produce the phenomena formerly ob-
served in filings of fteel, Scattered round the load-
ftone* i
You will pleafe farther to attend to this circum-
ftance, that the motion of the magnetic matter in
the vortex, is incomparably flower out of the load-
ftone, than in the magnetic tubes? where it is fepa-.
rated from the ether, after having been forced into
them by all the elaftic power of this laft fluid ; and
that, on efcaping, it mixes again with the ether, and
thereby lofes great part of it's motion, fo that it's
velocity in travelling to the extremities a a a is in-
comparably lefs than in the magnetic canals a by
though ftill very great with refpecl to us. You will
ealily comprehend, then, that the extremities of the
magnetic canals, by which the matter enters into the
loadftone and efcapes from it, are what we call it's
poles ; and that the magnetic poles of a loadftone
are
UPON EACH OTHER. 249
are by no means mathematical points, the whole
fpace, in which the extremities of the magnetic ca-
nals terminate, being one magnetic pole, as in the
loadftone reprefented figure 6, plate II. where the
whole furfaces A and B are the two poles.
Now, as thefe poles are diftinguifhed by the terms
north and fouth, yet we cannot affirm with certainty
whether it is by the north or fouth pole that the
magnetic matter enters into loadftones. You will
fee in the fecmel, that all the phenomena produced
by the admiflion and efcape, have fuch a perfect rc-
femblance, that it appears impoffible to determine the
queftion by experiments. It is, therefore, a matter
of indifference, whether we fuppofe that the magnetic
matter enters or efcapes by the north pole or by the
fouth.
Be it as it may, I fhall mark with the letter A, the
pole by which the magnetic matter enters, and with
B, that by which it efcapes, without pretending
thereby to indicate which is north or fouth. I pro-
ceed to the confideratkm of thefe vortices, in order
to form a judgment, how two loadftones act upon
each other.
Let us fuppofe (plate III fig. 2.) that the two load-
ftones A B andtf b are prefented to each other by the
poles of the fame name A, a, and their vortices will
be in a ftate of total oppofition. The magnetic
matter which is at C will enter at A and #, and thefe
two vortices attempting mutually to deftroy each
other, the matter which proceeds by E to enter at A
will meet at D that of the other loadftone, returning
bv
■25° ACTION OF MAGNETS.
by e to enter at a : from this muft refult a coflifion
of the two vortices, in which the one will repel the
other ; and this effect will extend to the loadftones
themfelves, which, thus fituated, undergo mutual
repulfion. The fame thing would take place, if the
two loadftones prefented to each other the other
poles B and b : for this reafon the poles of the fame
name are denominated hofiile, becaufe they actually
repel each other.
But if the loadftones prefent to each other the
poles of a different name, an oppofite effect, will en-
fue, and you will perceive that they have a mutual
attraction.
In figure 3, plate III. where the two loadftones pre-
fent to each other the poles B and a, the magnetic
matter which ifiues from the pole B, finding imme-
diately free admiflion into the other loadftone by it's
pole a, will not be diverted toward the fides, in order
to return and re-enter at A, but will pafs directly by
C into the other loadftone, and efcape from it at h,
and will perform the circuit by the fides d d to re-
enter, not by the pole a, but by the pole A, of the
other loadftone, completing the circuit by e f. Thus
the vortices of thefe two loadftones will unite, as if
there .were but one ; and this vortex being com-
preiled on all fides by the ether, will impel the two
loadftones toward each other, fo that they will ex-
hibit a mutual attraction.
This is the reafon why the poles of different names
are denominated/r/^/y, and thofe of the fame name
hojllle^ the principal phenomenon in magnetifm, in
as
MAGNETIC FORCE. 25I
as much as the poles of different names attract, and
thofe of the fame name repel each other.
jib November, 1761.
LETTER LXIV.
Nature of Iron and Steel. Manner of communicating t*)
them the Magnetic Force.
"AVING fettled the nature of the loadflone in
thefe canals which the magnetic matter can
o
pervade in only one direction, becaufe the valves
they contain prevent it's return in the contrary di-
rection, you can no longer doubt that they are the
continuation of thofe pores, (jig. 8, plate II.) whofe
fibres point in the fame direction, fo that feveral of
thefe particles, being joined in continuation, confti-
tute one magnetic canal. It is not fufheient, there-
fore, that the matter of the loadftone mould contain
many fimilar particles ; they muft likewife be dif-
pofed in fuch a manner as to form canals continued
from one extremity to the other, in order to grant
an uninterrupted tranfmiilion to the magnetic matter.
Iron and fteel, then, apparently contain fuch par-
ticles in great abundance; thefe are not, however,
originally difpofed in the manner I have been de-
fevibing, but are fcattered over the whole mafs, and
this difpofition is all they want to become real mag-
nets. In that cafe, they ftiil retain all their other
qualities, and are not diftinguifhable from other
maffes of iron and fteel, except that now they have,
beildes,
252 MANNER OF COMMUNICATING
befides, the properties of the loadftone : a knife and
a needle anfwer the fame purpofes, whether they
have or want the magnetic virtue. The change
which, takes place in the interior, from the arrange-
ment of the particles in the order which magnetifm
requires, is not externally perceptible ; and the iron
or fteel which has acquired the magnetic force, is
denominated an artificial magnet, to diftinguifh it
from the natural, which refembles a ftone, though
the magnetic properties are the fame in both. You
will have a curiofity, no doubt, to be informed in
what manner iron and fteel may be brought to, re-
ceive the magnetic force, and fo become artificial
magnets. Nothing can be more fimple; and the
vicinity of a loadftone is capable of rendering iron
fomewhat magnetic : it is the magnetic vortex which
produces this efrecl:, even though the iron and load-
ftone mould not come into contact.
However hard iron may appear, the particles
which contain the magnetic pores formerly repre-
fented, are very pliant in fubftance, and the fmalleft
force is fufiicient to change their fituation. The
magnetic matter of the vortex, entering into the
iron, will then eafily difpofe the firft magnetic pores
which it meets, following it's own direction; thofe
at leaft whofe fituation is not very different; and
having run through them, it will act in the fame
manner on the adjacent pores, till it has forced a
paffage quite through the iron, and thereby formed
fome magnetic canals. The figure of the iron con-
tributes greatly to facilitate this change; a lengthened
7 figure,
THE MAGNETIC FORCE. 253
figure, and placed in the fame direction with the
vortex, is moft adapted to it, as the magnetic matter,
in palling through the whole length, there difpofes a
great many particles in their juft fitimtion, in order
to form longer magnetic canals; and it is certain,
that the more there is the means of forming canals,
the longer they will be without interruption, the
more rapid will be the motion of the magnetic mat-
ter, and the greater the magnetic force.
It has likewife been remarked, that when the iron,
placed in a magnetic vortex, is violently fhaken or
ftruck, it acquires a higher degree of magnetifm
from this, becaufe the minute particles are by fuch
concuffion agitated and difengaged, fo as to yield
more eafily to the action of the magnetic matter
which penetrates them.
Placing accordingly a fmall bar of iron a b (plate
III. Jig. 4.) in the vortex of the loadftone A B, fo
that it's direction may nearly agree with that of the
current d e f of the magnetic matter, it will with eafe.
pafs thrpugh the bar, and form in it magnetic canals,
efpecially if, at the fame time, the bar is lhaken or
ftruck, to facilitate the tranfmiflion. It is likewife
obfervable, that the magnetic matter, which enters
at the pole A of the loadftone, and efcapes at the
pole B, will enter the bar at the extremity a and
efcape at the extremity b, fo that the extremity a
will become the pole of the fame name A, and b the
fame with B. Then taking this bar a b out of the
magnetic vortex, it will be an artificial magnet,
though very feeble, which will fupply it's own vor-
tex,
254 MAGNETIC FORCE.
tex, and preferve it's magnetic power, as long as it's
magnetic canals fhall not be interrupted. This will
take place fo much the more eafily that the pores of
iron are pliant ; thus the fame circumftance which
affifts the production of magnetifm, contributes like-
wife to it's deftruction. A natural magnet is not fo
eafily enfeebled, becaufe the pores are much clofer,,and
moreconfiderable efforts arerequifite to derangethem.
I fhall go more largely into the detail afterward;
I here propofe to explain the manner of moft na-
turally rendering iron magnetic ; though the force
which it thence acquires is very fmall, it will affift us
in comprehending this remarkable and almoffc uni-
verfal phenomenon. It has been obferved, that the
tongs and other implements of iron which are ufually -
placed in a vertical pofition, as well as bars of iron
fixed perpendicularly on fteeples, acquire in time a
very fenfible magnetic force. It has likewife been
perceived, that a bar of iron, hammered in a vertical
pofition, or heated red hot, on being plunged into
cold water in the fame pofition, becomes fomewhat
magnetic, without the application of any loadflone.
In order to account for this phenomenon, you have
only to recollect that the earth itfelf is a loadflone,
and confequentiy encompaffed with a magnetic vor-
tex, of which the declination and inclination of the
magnetic needle every where fliew the true direction.
If then a bar of iron remain long in that pofition,
there is no reafon to be furprized, fhould it become
magnetic. We have likewife feen, that the inclina-
tion of the magnetic needle is, at Berlin, 72 degrees, -
and
ACTION OF LOADSTONES ON IRON. 255
and as it is nearly • he fame all over Europe, this in-
clination differs only 18 degrees from the vertical
pofition; the vertical pofition, accordingly, differs
but little from the direction of the magnetic vortex :
a bar of iron, long kept in that pofition, will be at
laft penetrated with the magnetic vortex, and muft
confequently acquire a magnetic force.
In other countries, where the inclination is imper-
ceptible, v/hich is the cafe near the equator, it is not
the vertical, but rather the horizontal pofition which,
renders bars of iron magnetic, for their polition muft
correfpond to the magnetic inclination, if you would
have them acquire a magnetic force. I fpeak here
only of iron ; fteel is too hard for the purpofe, and
means more efficacious muft be employed to com-
municate the magnetic virtue to it.
Io/£ November, 1761.
LETTER LXV.
Aclion of Load/tones on Iron. Phenomena obfer-vabk on
■placing Pieces of Iron near a Loadjione.
nPHOUGH the whole earth may be confidered
A as a vaft loadftone, and as encompaffed with a
magnetic vortex, which every where directs the mag-
netic needle, it's magnetic power is, however, very
feeble, and much lefs than that of a very fmall load-
ftone : this appears very ftrange, coniidering the
enormous magnitude of the earth.
It arifes, undoubtedly, from our very remote dif-
tanc
2$6 ACTION OF LOADSTONES ON IRON.
tance from die real magnetic poles of the earth,
which, from every appearance, are buried at a great
depth below the fur face : now, however powerful a
loadflone may be, it's force is confiderable only when
it is very near ; and as it removes that fores gradu-
ally diminifhes, and at length difappears. For this
reafon, the magnetic force acquired in time by maffes
of iron fuitably placed in the earth's vortex is very
fmall, and indeed hardly perceptible, unlefs it is very
foft, and of- a figure adapted to the production of a
vortex, as has been already remarked.
This effect is much more confiderable near a load-
ftone of moderate fize : fmali maifes of iron fpeedily
Acquire from it a very perceptible magnetic force ;
they are likewife attracted toward the loadfione ;
whereas this effect is imperceptible in the earth's vor-
tex? and confifts only -in directing magnetic needles,
without either attracting them or increafing their
weight.
A mafs of iron plunged into the vortex of a load-
ftone, likewife prefents very curious phenomena,
which well deferve a particular explanation. Not
only is this mafs at firft attracted toward the load-
stone, but it too attracts other pieces of iron. Let
AB, (plate III. jig. 5. ) be a natural magnet, in the
vicinity of which, at the pole B, is placed the mais
of iron CD, and it will be foundthat this laft is ca-
pable of iupporting a bar of iron EF. Apply again
to this, at F, an iron ruler GH, in any pofition
whatever, fay horizontal, fupporting it at H, and
it will be found that the ruler is not only attracted
by
ACTION OF LOADSTONES ON IRON. 257
by the bar at F, but likewife capable of fupporting,
at H, needles as I K, and that thefe needles again
act on filings of iron L, and attract them.
The magnetic force may thus be propagated to
very confiderable distances, and even made to change
it's direction, by the different pofition of thefe pieces
of iron, though it gradually diminiihes. You are
perfectly fenlible, that the more powerful the load-
ftone AB is of itfelf, and the nearer to it the firft
mafs C D, the more confiderable likewife is the effect.
The late Mr. de Maupertuis had a large loadftone fo
powerful, that at the diftance even of feveral feet,
the mafs of iron CD continued to exert a very con-
fiderable force.
In order to explain thefe phenomena, you have
only to confider, that the magnetic matter which
efcapes rapidly, at the pole of the loadftone B, en-
ters into the mafs of iron, and difpofes the pores of
it to form magnetic canals, which it afterward freely
pervades. In like manner, on entering into the bar,
it will there too form magnetic canals, and fo on.
And as the magnetic matter, on ifTuing from one
body, enters into another, thefe two bodies raufi
undergo a mutual attraction, for the, fame reafon, as
I have before proved, that two loadftones, which
prefent their friendly poles to each other, mult be
attracted : and as often as we obferve an attraction
between two pieces of iron, we may with certainty
conclude, that the magnetic matter which ifTues from
the one is entering into the other, from the conti-
Vol. II. S nual
2$8 ACTION OF LOADSTONES ON IRON.
niial motion with which it penetrates thefe bodies.
It is thus that, in the preceding difpofition of the
bars of irGn, the magnetic matter in it's motion per-
vades all of them, and this is the only reafon of their
mutual attraction. .
The lame phenomena ftill prefent themfelves, on
turning the other pole A of the loadftone, by which
the magnetic matter enters, toward the mafs of iron.
The motion in this cafe becomes retrograde, and pre-
ferves the fame courfe ; for the magnetic matter
contained in the mafs of iron will then cfcape from
it, to pafs rapidly into the loadftone, and, in making
it's efcape, will employ the fame efforts to arrange
the pores in the mafs fuitably to the current, as if it
wererapidly entering into the iron. To this end,
therefore, the iron muft be fuihciently foft, and thefe
pores pliant, to obey the efforts of the magnetic mat-
ter. A difficulty will, no doubt, here occur to you ;
it will be afked, How do you account for the change
of direction of the magnetic matter, on entering into
another bar of iron ; and why is that direction re-
gulated according to the length of the bars, as it's
courfe is reprefented in the figure ? This is a very
important article in the theory of magnetifm, and it
proves how much the figure of the pieces of iron
contributes to the production, of the magnetic phe-
nomena.
To elucidate this, it muft be recollected, that this
fubtile matter moves with the utmoft eafe in the
magnetic pores3 where it is feparated from the ether ;
and
ACTION OF LOADSTONES ON IRON. 259
and that it encounters very confiderable obftacles,
When it efcapes from them, with all it's velocity, to
re-enter into the ether and the air.
Let us fuppofe that the magnetic matter, after
having pervaded the bar CD, (fig. 6. plate III.) en-
ters into the iron ruler EF, placed perpendicularly.
It would certainly, on it's firft admiffion, preferve the
fame direction, in order to efcape at m, unlefs it
found an eafier road in which to continue it's mo-
tion : but meeting at m the greateft obftruction, it
at firft changes it's direction, though in a very fmall
degree, toward F, where finding pores adapted to
the continuation of it's motion, it will deviate more
and more from it's firft direction, and travel through
the ruler EF in all it's length; and, as if the mag-
netic matter v/ere loth to leave the iron, i endea-
vours to continue it's motion there as long as poflible,
availing itfelf of the length of the ruler ; but if the
ruler were very fhort, it would undoubtedly efcape
at m. But the length of the ruler presenting it a
fpace to run through, it follows the direction EF,
till it is under the neceftity of efcaping at F, where
all the magnetic canals, formed according; to the
fame direction, no longer permit the fubtile mag-
netic matter to change it's direction, and return
along the ruler ; theie canals being not4 only filled
with fucceding matter, but, from their very nature,
incapable of receiving motion in an oppofite direc-
tion.
1 4$ November, 176'.
S 2 LETTER
l6o ARMING OF LOADSTONES.
LETTER LXVI.
Arming of "Loadftones.
"OU have juft feen how iron may receive the
magnetic current of a loadftone, convey it to
confiderable diftances, and even change it's direction.
To unite a loadftone, therefore, to pieces of iron, is
much the fame with increaiing it's fize, as the iron
acquires the fame nature with refpect to the mag-
netic matter ; and it being farther poftible by fuch
means to change the direction of the magnetic cur-
rent, as the poles are the places where this matter
enters the loadftone and efcapes, we are enabled to
conduct the poles at pleafure.
On this principle is founded the arming, or mount-
ing, of loadftones ; a fubject well worthy of your at-
tention, as loadftones are thereby carried to & higher
degree of ftrength.
Loadftones, on being taken from the mine, are
ufually reduced to the figure of a parallelopiped, or
rectangular parallelogram, with thicknefs as A A, BB,
(fig. 7. plate III. J of which the furface A A is the
pole by which the magnetic matter enters, and BB
that by which it efcapes. It is filled, then, the whole
length AB with canals a b, which the magnetic mat-
ter, impelled by the elaftic power of the ether, freely
pervades in the utmoft rapidity, without any mix-
ture of that fluid. Let us now fee in what manner
fuch a loadftone is ufually armed.
To
ARMING OF LOADSTONES. ••■ 261
To each furface A A and BB, (plate III fig. S.J
the two poles of the loadftone, are applied plates of
iron a a and' b b, terminating below in the knobs 3.
and % called the feet ; this is what we denominate
the armour of the loadftone, and when this is done,
the loadftone is faid to be armed. In this ftate, the
magnetic matter which would have efcaped at the
furface BB, paifes into the iron plate b b, where the
difficulty of flying off into the air, in it's own direc-
tion, obliges it to take a different one, and to flow
along the plate b b into the foot 23, and there it is
under the neceftity of efcaping, as it no longer finds
iron to affift the continuation of it's motion. The
fame thing takes place on the other fide ; the fubtile
matter will be there conducted through the foot 0,
from which it will pafs into the plate a a, changing
it's direction to enter into the loadftone, and to fly
through it's magnetic canals. For the fubtile mat-
ter, contained in the plate, enters firft into the load-
ftone ; it is followed by that which is the foot 3, re-
placed in it's turn by the external magnetic matter,
which being there impelled by the elafticity of the
ether, penetrates the foot 3 and the plate a a with a
rapidity whole vehemence is capable of arranging the
poles, and of forming magnetic canals.
Hence it is evident that the motion muft be the
fame on both fides, with this difference, that the
magnetic matter will enter by the foot % and efcape
by the foot 2d, fo that in thefe two feet we now find
the poles of the armed loadftone ; and as the poles
formerly diffufed over the furfaces AA and BB are
S 3 now
l62 ARMING OF LOADSTONES.
now colle&ed in the bafes of the feet 3 and 23, it is
naturally to be fuppofed that the magnetic force muft
be conliderably greater in thefe new poles.
In this ft ate, accordingly 3 the vortex will be more,
eafily formed. The matter efcaping from the foot
S5 will, with the utmoft facility, return to the foot 3,
palling through C ; and the rell of the body of the
loadftone will not be encompafled by any vortex ;
unlefs perhaps a fmall quantity of magnetic matter,
fliouid efcape from the plate bb9 from it's not being
able to change the direction fo fuddenly : and unlefs
a fmall quantity ihould find admiftion by the plate
a a, which, in that cafe, might produce a feeble vor-
tex, whereby the fubtile matter would be immedi-
ately conducted from the plate b b to a a ; however,
if the armour be well fitted, this fecond vortex will
be alinoft imperceptible, and confequently the cur-
rent between the feet is fo much the ftronger.
The principal direction for arming loadftones, is
carefully to poliih both furfaces of the loadftone A A
and BB, as well as the plates of iron, fo that, on
applying them to the loadftone, they may exactly
touch it in every point, the fubtile matter palling
eafily from the loadftone to the iron, when unob-
itructed by any intervenient matter : but if there be
a vacuum, or a body of air, between the loadftone
and the plates, the magnetic matter will lofe almoft
all it's motion, it's current will be interrupted, and
rendered incapable of forcing it's paflage' through
the iron, by forming magnetic canals in it.
The fort eft and moli ductile iron is to be prefer-
red
ARMING OF LOADSTONES. 263
red for the conftruction of fuch armour, becaufe it's
pores are pliant, and calily arrange themfelves in
conformity to the current of the magnetic matter :
iron of this defcription, accordingly, appears much
adapted to the production of a fudden change in the
direction of the current : the magnetic matter, too,
feems to affect a progrefs in that direction as long as
poilible, and quits it not, till the continuance of it's
motion through that medium is no longer practi-
cable : it prefers making a circuit to a premature de-
parture : a thing that does not take place in the
loadftone itfelf, in which the magnetic canals are al-
ready formed, nor in iteel, whofe pores do not fo
eafily yield to the efforts of a magnetic current. But
when thefe canals are once formed in fteel, they are
not fo ealily deranged, and much longer retain their
magnetic force ; whereas foft iron, whatever force it
may have exerted during it's junction with a load-
ftone, lofes it aim oft entirely on being disjoined.
Experience muft be confulted as to the other cir-
cumftances of arming loadftones. Reflecting the
plates, it has been found, that a thicknefs either too
great or too fmail is injurious ; but for the molt
part, the beft adapted plates are very thin, which
would appear ftrange, did we not know that the
magnetic matter is much more fubtile than ether,
and that, confequently, the thinneft plate is fufficient
to receive a very great quantity of it.
1 1th i\ 'member, r 76 1 .
S ± LETTER
264 ACTION AND FORCE OF
LETTER LXVII.
Aclion and Force of armed Loadfkones.
T the feet of it's armour, then, a loadftone ex-
erts it's greateft force, becaufe there it's poles
are collected ; and each foot is capable of fupporting
a weight of iron, greater or lefs in proportion to the
excellency of the loadftone.
Thus a loadftone A A, B B, (plate III. fig* 9.)
armed with plates of iron a a and b b, terminating
in the feet il and 35, will fupport by the foot 3 not
only the iron ruler CD, but this laft will fupport
another of fmaller lize EF, this again another ftill
fmaller GH, which will in it's turn fupport a needle
I K, which, finally, will attract filings of iron L ;
becaufe the magnetic matter runs through all thefe
pieces to enter at the pole & ; or if it were the other
pole, by which the magnetic matter iffues from the
loadftone, it would in like manner run through the
pieces CD, EF, GH, IK. Now, as often as the mat-
ter is tranfmitted from one piece to another, an at-
traction between the two pieces is obfervable, or
rather, they are impelled toward eacli other by the
furrounding ether, becaufe the current of the mag-
netic matter between them diminiihes the preflure
of that fluid.
When one of the poles of the loadftone is thus
loaded, it's vortex undergoes a very renarkab ej
change of direction j for as, without this weight, the
magnetic
ARMED LOADSTONES. 265
magnetic matter which iffucs from the pole 2?, di-
recting around it's courfe, would flow toward the
other pole 9L\ and as now the entrance into this pole
is fufliciently mpplied by the pieces which it fup-
ports, the matter ifiuing from the pole 25 muft take
quite a different road, which will at length conduct,
it to the laft piece IK. A portion of it will, un-
doubtedly, be likewife conveyed toward the laft but
one GH, and toward thofe which precede it, as
thofe which follow, being fmaller, do not fupply in
fufilcient abundance thofe which go before, but the
vortex will always extend to the laft piece. By thefe
means, if the pieces are well proportioned to each
other, in length and thicknefs, the loadftone is ca-
pable of fupporting much more, than if it were
loaded with a fmgle piece, in which the figure like-
wife enters principally into conlideration. But in
order to make it fuftain the greateft poffible weight,
we muft contrive to unite the force of both poles.
For this purpofe, there is applied to the two poles
% and 25, (plate IV. fig. i.) a piece of foft iron CD,
touching the bafes of the feet in all points, and whofe
figure is inch, that the magnetic matter which iirues
from 23 fhall find in it the moil commodious pailage
to re-enter at the other extremity &, Such a piece
of iron is called the fupporter of the loadftone ; and
as the magnetic matter enters into it, on iiluing
from the loadftone at 23, and enters into the other
pole cr on iiluing from the fupporter, the iron v. ill
be attracted to both poles at once, and conil
adhere to them with great force. In order to know
how-
200 ACTION AND FORCE OF
how much power the loadftone exerts, there is af-
fixed to the fupporter at the middle F, a weight P,
which is increafed till the loadftone is no longer ca-
pable of mftaining it, and then that weight is faid
to counterbalance the magnetic power of the load-
ftone : this is what you are to underftand when told,
that fuch a loadftone carries ten pounds weight, fuch
another thirty, and fo on. Mahomet's coffin, they
pretend, is fupported by the force of a loadftone ;
a thing by no means impoflible, as artificial magnets
have already been conftructed which carry more than
100 pounds weight.
A loadftone armed with it's fupporter lofes nothing
of the magnetic matter, which performs it's complete
vortex within the loadftone and the iron, fo that
none of it efcapes into the air. Since, then, mag-
netifm exerts it's power only in fo far as the matter
efcapes from one body to enter into another ; a load-
ftone whofe vortex is fhut up, mould no where exert
the magnetic power ; neverthelefs when it is touched
on the plate at a with the point of a needle, a very
powerful attraction is perceptible, becaufe the mag-
netic matter being obliged fuddenly to change it's
direction, in order to enter into the canals of the
loadftone, finds a more commodious paifage by run-
ning through the needle, which will confequently be
attracted to the plate a a. But, by that very thing,
the vortex will be deranged inwardly ; it will not
flow lo copioufly into the feet ; and if you were to
apply fi^eral needles to the plate, or iron rulers ftill
more powerful, the. current toward the feet, would
2 be
ARMED LOADSTONES. l6j
be entirely diverted, and the force which attracts
the fupporter would altogether difappear, fo that it
would drop off without effort. Hence it is evident,
that the feet lofe their magnetic power in proportion
as the loadftone exercifes it's force in other places,
and thus we are enabled to account for a variety of
very furprizing phenomena, which, without the
theory, would be abfolutely. inexplicable.
This is the proper place for introducing the expe-
riment which demonftrates, that after having applied
it's fupporter to an armed loadftone, you may go on,
from day to day, increafing the weight which it is
able to fuftain, till it, at length, fhall exceed the
double of what it carried at firft. It is neceffary to
fliew, therefore, how the magnetic force may, in
time, be increafed in the feet of the armour. The
cafe aJDOve defcribed, of the derangement of the vor-
tex, allures us, that at the moment when the fup-
porter is applied, the current of the magnetic mat-
ter is full abundantly irregular, that a confiderable
part of it is ftill efcaping by the plate b b, and that
it will require time to force magnetic canals in the
iron ; it is likewife probable that, when the current
fhall have become more free, new canals may be
formed in the loadftone itfelf, considering that it con-
tains, befide thofe fixed canais, moveable poles, as.
iron does. But on violently feparating the fupporter
from the loadftone, the current being difturbed, and
thefe new canals in a great meafure deftroyed, the
force is fuddenly rendered as fmall as at the begin-
ning ; and fome time muft intervene before thefe ca-
nals,
2.68 MANNER OF COMMUNICATING
nals, with the vortex, can recover their preceding
ftate. I once conftrucfced an artificial magnet, which
at firft. could fupport only ten pound weight, 'and,
after fome time, I was furprized to find that it could
fupport more than, thirty. It 'is remarked, chiefly
in artificial mas-nets, that time alone ftrensrthcns
them confiderably, but that this increafe of force lafts
only till the fupporter is feparated from it.
2 xjl ~N<memberi 1 76 1 .
-=S9 9-K-«!
LETTER LXVIII.
The Manner of communicating to Steel the Magnetic
Force, and of magnetizing Needles for the Compafs :
the Simple Touch, it's Defects ; Means of remedying
thefe.
' AVING explained the nature of magnets in ge-
■ neral, an article as curious as interefting ftill
remains, namely, the manner of communicating to
iron, but efpecially to fteel, the magnetic power, and
even the higheft degree pofFible, of that power.
You have feen that, by placing iron in the vortex
of a loadilone, it acquires a magnetic force, but which
almoft totally difappears, as foon as it is removed out
of the vortex ; and that the vortex of the earth alone .
is capable, in time, of impreiftng a flight magnetic
power upon iron ; now, fteel being Larder than iron,
and almoft entirely infenlible to this action of the
magnetic vortex, more powerful operations rnuft be
employed
THE MAGNETIC FORCE. id)
employed to magnetize it ; but then it retains the
magnetic force much longer.
For this purpofe we muft have recourfe to touch-
ing, and even to friction. I begin, therefore, with
explaining the method formerly employed, for mag-
netizing the needles of compafies ; the whole opera-
tion confifted in rubbing them at the pole with a
good loadftone, whether naked or armed.
■■ The needle a b c (plate IV. f.g. i.) was laid on
a table ; the pole B of the loadftone was drawn
over it, from b toward a, and, being arrived at the
extremity a9 the loadftone was raifed aloft, and
brought back through the air to b ; this operation
was repeated fever al times together, particular care
being taken that the other pole of the loadftone
fhould not come near the needle, as this would have
difturbed the whole procefs. Having feveral times
drawn the pole , B of the loadftone over the needle
from b to a, the needle had become magnetic, and
the extremity b of the fame name with that of the
loadftone with which it had been rubbed. In order
to render the extremity b the north pole, it would
have been neceffary to rub with the pole of this name
in the loadftone, proceeding from b to a ; but in
rubbing with the fouth pole, the progrefs muft be
from a to b.
This method of rubbing or touching, is denomi-
nated the fimple touchy becaufe the operation is per-
formed by touching with one pole only ; but it is
extremely defective, and communicates but very little
power
fJQ MANNER OF COMMUNICATING
power to the needle, let the lo^dftone be ever fo ex-
cellent ; accordingly it does not fucceed^ when the
fteel is carried to the higheft degree of hardnefs,
though this be the ftate beft adapted to the retention
of magnetifm. You will yourfelf readily difcern the
defects of this method by thejimple touch.
Let us fuppofe that B is the pole of the lOadftonC
from which the magnetic matter ihues, as the effect
of the two poles is fo fimilar that it is impoffible to
perceive the flighteft difference : having refted the
pole on the extremity b of the needle, the magnetic
matter enters into it with all the rapidity with which
it moves in the loadftone, incomparably greater thai!
that of the vortex which is in the external air. But
what will become of this matter in the needle ? It
cannot get out at the extremity b, it will, therefore*
make an effort to force it's way through the needle
toward a, and the pole B moving in the fame direc-
tion, will an" iff this effort ; but as foon as the pole B
fhall arrive at a, the difficulty of efcaping at the ex*
tremity a will occafion a contrary effort, by which
the magnetic matter will be impelled from a toward
b ; and before the firft effect is entirely deftroyed,
this laft cannot take place. Afterwards, when the
pole B is again brought back to the extremity b, this
laft effect is again deftroyed, but without producing,
however, a current in the contrary direction from b
toward a ; and confequently, when the pole B fhall
have got beyond c in it's progrefs toward a, it will
more eafily produce a current from a to b, efpecially
if
THE MAGNETIC FORCE. 27 T
if yon prefs more hard on the half c a : hence it is
•clear, that the needle can have acquired only a fmall
derrce of the magnetic power.
Some, accordingly, rub only the half c a (plate III.
fig. 10.) proceeding from c to a, and others touch
only the extremity a of the needle, with the pole B
of the loadftone, and with nearly the fame fuccefs.
But it is evident that the magnetic matter which
enters by the extremity a only, is incapable of acting
with fuflicient vigor on the pores of the needle, for
arranging them conformably to the laws of mag-
netifm ; and that the force impreffed by this method
mult be extremely fmall, if any thing, when the fteel
is very much hardened.
It appears to me, then, that thefe defects of the
fimple touch might be remedied in the following man-
ner ; of the fuccefs of which I entertain no doubt,
though I have not yet tried it, but am confirmed in
my opinion by experiments which I have made.
I would cafe the extremity b of the needle, (plate
HI. fig. 1 1 .) in a ruler of foft iron E F ; and I lliould
think it proper to make that ruler very thin, and as
ftraight as poilible, but the extremity muft be exactly
applied in all points, and even fitted to a groove per-
fectly adjufted for it's reception. On refting the pole B
of the loadftone upon the extremity b of the needle,
the magnetic matter which enters into it, meeting
fcarcely any difficulty in it's progrefs through the
iron ruler, will at once purfue it's courfe in the di-
rection b d ; and in proportion as the pole advances
toward a, the magnetic matter, in order to continue
this
272 MAGNETIC FORCE.
this courfe, has only to arrange the pores on which
it immediately acts ; and having reached a, all theie
pores, or at leaft by far the greater part of them, will
be already difpofed conformably to that direction.
"When you afterwards re-commence the friction at
the extremity b, nothing is deftroyed, but you con-
tinue to perfect the current of the magnetic matter,
following the fame direction b d by likewife arrang-
ing the pores which refilled the firft operation, and
thus the magnetic canals, in the needle, will always
become more perfect. A few ftrokes of the pole B
will be fufficient for the purpofe, provided the load-
ftone is not too weak : and I have no doubt, that the
belt tempered fteel, that is, rendered as hard as pof-
fible, would yield to this method of operating ; an
unfpeakable advantage in the conftruction of com-
paffes, as it has been found that ordinary needles fre-
quently lofe, by a flight accident, all their magnetic
power ; by which fhips at fea would be expofed to
the greateft dangers, if they had not others in re-
ferve. But when needles are made of well tempered
fteel, accidents of this kind are not fo much to be ap-
prehended ; for if a greater force is requifite to ren-
der them magnetic, in return they preferve the power
more tenacioufly.
%\th November , 1761.
LETTER
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MAGNETIC MATTER. 273
LETTER LXIX.
On the Double Touch. Means of preferving the Mag-
netic Matter in magnetized Bars.
TNSTEAD of this method of magnetizing iron or
-*- fteel by thejimple touchy by rubbing with one pole
only of the loadftone, we now employ the double
touch, in which we rub with both poles at once,
which is eafily done by means of an armed load-
ftone.
Let E F, (plate IV. jig. 4. J be a bar of iron or fteel
which you wifh to render magnetic. Having fixed
it fteadily on a table, you prefs upon it the two feet
A and B of an armed loadftone. In this ftate, you
will eafily fee that the magnetic matter, which iffues
from the loadftone by the foot B muft penetrate into
the bar, and would diffufe itfelf in all directions, did
not the foot A, on it's fide, attract, the magnetic mat-
ter contained in the pores of the bar. This evacu-
ation, therefore, at d will determine the matter,
which enters by the pole B, to take it's courfe from
c toward d. provided the poles A and B are not too
remote from each other. Then the magnetic cur-
rent will force it's way in the bar, in order to pafs
from the pole B to the pole A, difpofmg it's pores to
form magnetic canals ; and it is very eafy to difco-
ver whether this is taking place ; you have only to
Gbferve if the loadftone is powerfully attracted to
You II. T th|
274 MEANS OF PRESERVING
the bar, which never fails, if the bar is of foft iron,
as the magnetic matter eafily penetrates it. But if
the bar is of fteel, the attraction is frequently very
fmall, a proof that the magnetic matter is incapable
of opening for itfelf a pafTage from c to d ; hence it
is to be concluded that the loadftone is too feeble, or
that the dif lance between it's two poles is too great :
in this cafe it would be neceflary to employ a load-
ftone more powerful, or whofe feel: are nearer, or,
finally, the armour of the loadftone ought to be
changed into the form reprefented in plate IV. Jig. 3.
But here is a method for remedying this incon-
venience.
Having difpofed, at fmall intervals c d (plate IF,
Jig. 4.) the powers conformably to magnetifm, the
loadftone muft be feveral times drawn backward and
forward over the baf, from one extremity to the
other, without taking it ■ off, till you perceive that
the attraction no longer increafes \ for it is undoubt-
edly certain , that attraction is increafed in proportion
to the increafe of the magnetic force. The bar E F
will be magnetized by this operation, in fuch a man*
ner that the extremity E, toward which the pole A
was turned, will be the friendly pole of A, and con»
fequently of the fame name with the other pole B.
Again, on removing the loadftone, as magnetic ca-
nals are formed the whole length of the bar, the
magnetic matter diffufed through the air will force
a paffage through thefe canals, and will make the
bar a real magnet, - It will enter by the extremity a
and
THE MAGNETIC MATTER. 275
and efcape by the extremity b, from whence a part,
at leaft, will return to a, and will form a vortex fuch
as the nature of the bar permits.
I take this occafion to remark, that the formation
of a vortex is abfolutely neceffary to the increafe of
magnetifm ; for if all the magnetic matter which
goes out at the extremity b were to fly off, and be
entirely difperfed, without returning to a, the air
would not fupply a mfficient quantity to the other
extremity a, which muft occafion a diminution of
the magnetic force. But if a confiderable part of
that which efcapes at the extremity b returns to <?,
the air is abundantly able to fupply the remainder,
and perhaps ftill more, if the magnetic canals of the-
bar are capable of receiving it j the bar will there-
fore, in that cafe, acquire a much greater magnetic
force,
This consideration leads me to explain how it is
poflible to keep up the magnetic matter in magne-
tized bars. The object being to prevent the mag-
netic matter, which pervades them, from difperfmg
in the air, thefe bars are always difpofed in pairs of
exactly the fame fize. They are placed on a table,
in a parallel fituation, fo that the friendly poles, or
thofe of different names, mould be turned to the
fame fide as in fig. 5,
M M and N N reprefent .the two bars, whofe
friendly poles a b, b a are turned the fame way.
To prevent miftake, a mark x is made on each bar,
at the extremity where the north pole is, and to
both ends is applied a piece of foft iron E E and F F,
T 2 for
276 MEANS OF PRESERVING
for receiving the magnetic current. In this manner,
the whole magnetic matter, which pervades the bar
M M, and which iffu.es at the extremity b, paffes into
the piece of iron E E, where it eafily makes it's way,
to enter at the extremity a of the other bar N N,
from which it will efcape at the extremity b into the
other piece of iron F F, which re-conveys it into the
firft bar M M by the extremity a. Thus the mag?
netic matter will continue to circulate, and no part
of it efcape ; and even in cafe there mould not be at
firft a fufficient quantity to fupply the vortex, the
air will fupply the deficiency, and the vortex will
preferve all it's force in the two bars.
This difpbfition of the two bars may likewife be
employed for magnetizing both of them at once.
The two poles of a loadftone muft be drawn over
the two bars, pafling from the one to the other by
the pieces of iron, and the circuit muft be feveral
times performed, carefully obferving that the two
poles of the loadftone A and B be turned as the
figure -directs.
This method of magnetizing two bars at once, muft
be much more efficacious than the preceding, as
from the very firft circuit performed by the load-
ftone, the magnetic matter will begin to flow through
the two bars by means of the two pieces of iron.;
Afterwards, by repeated circuitous applications of
the loadftone to the bars, a greater quantity of pores
will be arranged in them conformably to magnetifm,
and more magnetic canals will be opened, by which
the vortex will be more and more ftrengthenedj,
without
THE MAGNETIC MATTER. 2/7
without undergoing any diminution. If the bars
are thick, it would be proper to turn and rub them,
in the fame manner, on the other furfaces, in order
that the magnetic action may penetrate them tho-
roughly.
Having obtained thefe magnetic bars M M, N N,
(plate IV. fg. 6.) they may be employed, in place of
the natural loadftone, for magnetizing others. They
are joined together a-top, fo that the two friendly
poles a b may touch each other ; and the other two
poles below, b and a, are feparated as far as it is
thought proper. Then we rub with the two under
extremities, which fupply the place of the two poles
of a loadftone, two other bars E F in the manner
which I have above explained.
As thefe two bars are joined in the form of com-
panies, we have the advantage of opening the lower
extremities as much or as little as we pleafe, which
cannot be done with a loadftone j and the magnetic
current will eafily pafs a-top, where the bars touch
each other, from the one to the other. A fmall
piece of foft iron P might likewife be applied there,
the better to keep up the current : and in this man-
ner you may eafily and fpeedily magnetize as many
double bars as you pleafe.
2 Ztb N member, 1 7 6 1 .
T 3 LETTER
2J% MAGNETIC FORCE COMMUNICATED
LETTER LXX.
The Method of communicating to Bars of Steel a very
great Magnetic Force , by Means of other Bars which
have it in a very inferior Degree.
^IpHOUGH this method of magnetizing by the
■*- double touch be preferable to the preceding, the
magnetic power, however, cannot be carried beyond
a certain degree. Whether we employ a natural
loadflone, or two magnetic bars for rubbing other
bars, thefc laft will never acquire fo much force as
the firft ; it being impoffible that the effect mould be
greater than the caufe.
If the bars with which we rub have little force,
thofe which are rubbed will have frill lefs : the rea-
fon is evident ; for as bars deftitute of magnetic force
never could produce it in others, fo a moderate de-
gree of force is incapable of producing one greater
than itfelf, at leaft by the method which I have been
defcribing.
But this rule is not to be taken in the frrict. inter-
pretation of the words, as if it were literally impof-
fible to produce a greater magnetic force by the
affiftance of a fmaller. I am going, to point out a
method by which the magnetic power may be in-
creafed almoft as far as you pleafe, beginning with
the fmalleft degree poffible. This is a late difcovery,
which merits fo much the more attention that it
throws much light on a very difficult fubjecl, the
nature of magnetifm.
Sup'poiing
TO BARS OF STEEL. 279
Supposing me poiTefled of a very feeble loadftone,
or, for want of a natural magnet, of bars of iron ren-
dered fomewhat magnetic, merely by the vortex of
the earth, as I explained it in a preceding letter, I
then provide myfelf with eight bars of fteel very
fmall and not hardened, in order the more eafily to
receive the fmall degree of magnetic power which
the feeble loadftone, or flightly magnetized bars, are
capable of communicating, by rubbing each pair or
couple in the manner I formerly defcribed. Having
then eight bars, magnetic but in a very fmall degree,
I take two pair, which I join together in the manner
reprefented, plate IV. Jig. 7.
By uniting the two bars by the poles of the fame
name, I form but one of double the thicknefs, and
with which I form the compafs A C and B D ; the
better to keep up the magnetic current, a piece of
foft iron P may be applied at the top C D. The legs
of the compafs may be feparated as far as is judged
proper, and I rub with them, one after the other,
the remaining bars, which will thereby acquire more
power than they had before, becaufe the powers of
the firft are now united. I have now only to join
thefe two pair newly rubbed, in the fame manner,
and by rubbing with them one after the other, the
two pair firft employed, and the power of thefe will
be confiderably increafed. I afterwards join thefe
two pair together, and go on rubbing others in order
to augment their magnetic force, and ftili . two pair
with two pair alternately ; and by repeating this
operation the magnetic power may be carried to fuel*
T 4 a degree.
2&Q MAGNETIC FORCE COMMUNICATED
a degree, as to become infufceptible of farther in-
creafe, even by continuing the operation* When
we have more than four pair of fuch bars, inftead of
two pair, three may be joined together for the pur-
pole of rubbing others ; they will thereby be fooner
carried to the higheft degree poJTible.
The greateft obitacles are, therefore, furmounted,
and, by means of fuch bars joined together by two
or more pairs, we may rub others of fteel properly
hardened, and which may be either of the fame fize,
or hall greater than the firft, to which the greateft
power of which they are fufceptible may be thus
communicated.
Beginning with fmall bars fuch as I have defcribed,
tliefe operations may be fuccellively applied to bars
of an enormous fize, and made of the hardeft iteel,
which is lefs liable to lofe the magnetic power. Only
it is to be obferved, that fof the purpofe of rubbing
large bars, feveral pairs ought to be joined together,
whole united weight mould be at leaft double that of
the large one. But it would always be better to
proceed by degrees, and to rub each fpecies of bars
with bars not much fmaller than themfelves, or it may
be fuillcient to join 'at moil two pair : for when we
are obliged to join more than two pair, the extremi-
ties with which the friction is performed will extend
too far, and the magnetic matter, which pafles that
way, will itfelf prevent it's being directed conformably
to the direction of the bar that is rubbed *, and the
rather, that it enters the bar perpendicularly, whereas
it neccffarily mould take a horizontal direction.
In
TO §ARS OF STEEL. 2 Si
In order to facilitate this change of direction, it is
proper that the magnetic matter mould be led to it
in a fmall fpace, and in a direction already approach-
ing to that which it ought to take within the bar
which we are going to rub. The following method,
I think, might be effectual for this purpofe.
Plate IV. Jig. 8. reprefents five pair of bars M M,
N N, joined together, but not in the form of a com-
pafs. There is at top a bar of foft iron C D, to keep
up the vortex ; below, I do not rub immediately
with the extremities of the bars, but I cafe thefe ex-
tremities on each iide in a foot of foft iron, fattening
them to it with fcrews marked O. Each foot is bent
at A and B, fo that the direction of the magnetic
matter, which freely pervades thefe feet, already has
a confiderable approximation to the horizontal, fo
that in the bar to be rubbed E F it has no need
greatly to change it's direction. I have no doubt
that, by means of thefe feet, the bar E F will receive
a much greater magnetic power, than if we rubbed
immediately by the extremities of the bars, the depth
of whofe vertical direction naturally oppofes the for-
mation of horizontal magnetic canals in the bar E F.
It is likewife poffible, in practifing this method, to
contract or extend the diftance of the feet A and B,
at pleafure.
I muft farther obferve, that when thefe bars lofe,
in time, their magnetic power, it is eafily reftored by
the fame operation.
iji December y 1 761.
LETTER
2B.2 ARTIFICIAL MA**J£YS<
LETTER LXXI.
Conjirualon of artificial Magnets in Form of a Horfe Shoe*
7HQEVER willies to make experiments on
i the properties of the loadftone* ought to be
provided with a great number of magnetic bars,
from a very final!, up to a very large fize* Each
may be confidered as a particular magnet, having it's
two poles, the one north and the other fotitha
You muft have confidered it as extremely remark-
able, that by the interposition of the magnetic power,
the feebleft which can be fupplied by a wretched na-
tural loadftone, or by a pair of tongs in the chimney
corner, which have acquired by length of time a
fmail portion of magnetifm, we fliould be enabled to
increafe that power to fuch a degree, >as to commu-
nicate to the largeft bars of ft eel, the higheft degree
of magnetic force of which they are fufceptibie. It
would be neediefs to add that, by this method, we
are enabled to conftru ct. the bed magnetic needles,
not only much larger than the common, but made
of a fteel hardened to the higheft degree, which ren-
ders them more durable. I have only a few words
to add on the conftruclion of artificial magnets, which
have ufually the form of a horfe-fhoe, as you muft
no doubt have feen.
Thefe artificial magnets anfwer the fame purpofes,
On every occafion, as the natural, with this advantage
in their favour, that we can have them much more
powerful,
ARTIFICIAL MAGNETS. 283
powerful, by giving them a fufficient magnitude.
They are made of well-tempered ftecl, and the figure
of a horfe-fhoe feems the moft proper for keeping up
the vortex. When the mechanic has finifhed his
work, we communicate to it the greateft degree of
magnetic power of which it is fufceptible, by means
of the magnetic bars of which I have given a defcrip-
tion. It is evident that the greater this magnet is,
the larger muft be the bars we employ ; and this is
the reafon why we ihould be provided with bars of
all fizes.
In order to magnetize a horfe-fhoe H I G, (plafe
IV. jig. 9.) which ought to be of fteel well tempered,
we place on the table a pair of magnetic bars A C
and BD, with their fupporters of foft iron applied on
both fides, but of which the figure reprefents only
one E F, the other having been removed to make
way gradually for the application of the feet of the
horfe-fhoe, as you fee. In this ftate, the magnetic
matter, which pervades the bars, will make ftrong
efforts to pafs through the horfe-fhoe, the poles of the
bars being adapted magnetically to thofe of the horfe-
fhoe ; but confidering the hardnefs of tempered fleel,
it will not be fufficient to arrange the pores and open
for itfelf a paffage. The fame means, therefore, muft
be employed to this effect, which were prefcribed for
the magnetizing of bars. We take a cempafs formed
of another pair of magnetic bars, and rub them in
the fame manner over the horfe-fhoe ; magnetic
canals will thereby be opened, and the fubtiie matter
of the bars, by pervading it, will form the vortex of
that
284 ARTIFICIAL MAGNETS.
that flaidi Particular care mult be taken, in this
operation, that the legs of the compafs, in palling
over the horfe-fhoe, do not touch the extremities A
and B of the bars ; for this would difturb the current
of the magnetic matter, which would pafs immedi-
ately from the bars into the legs of the compafs ; or,
the vortices of the bars and of the compafs would
mutually derange each other.
The horfe-fhoe will thereby acquire very great
power, being pervaded by an impetuous magnetic
current. All that remains to be done, is to detach
the bars, without deranging the current. If they are
feparated violently, the magnetic vortex will be de-
ftroyed, and the artificial magnet will retain very
little power.
The canals being kept up no longer than the mag-
netic matter pervades them, it mull be concluded,
that the particles which form thefe canals are in a
forced Hate, and that this ftate fubfifts only while the
vortex acts ; and that as foon as it ceafes, thefe par-
ticles, by their elaflicity, will deviate from their forced
fituation, and the magnetic canals will be interrupted
and deftroyed. This we clearly fee in the cafe of
foft iron, whofe pores are quickly arranged, on the
approach of a magnetic vortex, but retain fcarcely any
magnetic power, when removed out of the vortex.
This proves that the pores of iron are moveable, but
endowed with an elaflicity which changes their fitua-
tion, as foon as force ceafes. It requires length of
time to fix certain pores in the polition impreffed on
them by the magnetic force, which takes place chiefly
6 in
ARTIFICIAL MAGNETS. 285
in bars of iron long expofed to the vortex of the earth.
The pores of fleel are much lefs flexible, and better
fupport the ftate into which they have been forced ;
they are, however, liable to forne derangement, as
foon as force ceafes to act on them, but this derange-
ment is lefs in proportion to the harcjnefs of the fteel.
For this reafon, artificial magnets ought to be made
of the hardeft fteel: were they to be made of iron,
they would immediately acquire, on being applied to
magnetic bars, a very great degree of power ; but
the moment you detach them, all that power would
difappear. Great precaution muft, therefore, be em-
ployed, in feparating from the bars magnets com-
pofed of well-tempered fteel. For this purpofe, be-
fore the feparation,you prefs the fupporter, which is
of very foft iron, in the direction of the line M N,
(plate IV. Jig. 10.) taking particular care not to touch
the bars with it, for this would mar the whole pro-
cefs, and oblige you to repeat the operation. On the
application of the fupporter, a confiderable portion of
the magnetic matter which is circulating in the mag-
net G H T, will make its way through the fupporter,
and form a feparate vortex, which will continue after
the magnet is detached from the bars.
^ Afterwards you prefs the fupporter flowly forward
over the leers of the magnet to the extremities, as re-
prefented in the figure, and in this ftate permit it to
reft for fome time, that the vortex may be allowed
to fettle. The fupporter is likewife furniftied with a
weight P, which may be increafed every day ; it being
always.
286 ON DIOPTRICKS.
always underftood, that the fupporter is to be fo
perfectly adjufted to the feet of the magnet, as to
touch them in all points. '
§tb December, 1761.
LETTER LXX I.
On Diopf ricks ; Instruments which that Science fupplies :
of Tele/copes and Micro/copes. Different Figures given
to Glajfcs or Lenfcs.
THE wonders of dioptricks will now, I think,
furnilh a fubjecl worthy of your attention.
This fcience provides us with two kinds' of inflru-
rnents compofed of glafs, which ferve to extend our
iphere of vilion, by difcovering objects which would
efcape the naked eye.
There are two cafes in which the eye needs afiift-
ance : the firft is, when objects are too diftant to ad^
mit of our feeing them diflinctly ; fuch are the hear
venly bodies, refpecling which, the mod important
difcoveries have been made by means of dioptrical
inftruments. You will pleafe to recollect what I
have faid, concerning the fatellites of Jupiter, which
affift us in the difcovery of the longitude : they are
vilible only with the aid of good telefcopes, and thofe
of Saturn require telefcopes of a ftill better conftruc*
tion.
There are, befides, on the furface of the earth ob.
je&s very diftant, which it is impoiiible for us.to fee,
and
ON DIOPT RICKS. .: 9 J
and to examine in detail, without the afTiftancc of
telefcopes, which reprefent them to us in the fame
manner, as if they were near. Thcfe dioptrical-
glaiTes or inftruments, for viewing uiftaut bodies, are
denominated by the term we have already employed,
tele/copes or perfpectives.
The other cafe, in which the eye needs aftiitancc,
is when the object, though fufficiently near, is too
fmall to admit of a diftinct examination of it's parts.
If we wifhed, for example, to difcover all the parts
of the leg of a fly, or of any infect ftill fmaller : if
we were difpofed to examine the minuter particles
of the human body, fuch as the fmalleft fibres of the
mufcles, of the nerves, it would be impoflible to fuc-
ceed without the help of certain inftruments called
micro/copes, which reprefent fmall objects in the famq
manner as if they were a hundred or a thoufand
times greater.
Here then are two kinds of inftruments, telefcopes
and microfcopes, furnilhed by dioptricks for afftiting
the weaknefs of our fight. A few ages only have
elapfed fince thefe inftruments were invented ; and
from the era of that invention muft be dated the
moft important difcoveries in aftronomy, by means
of the telefcope, and in phyfics by the microfcope.
> Thefe wonderful effects are produced merely by
the figure given to bits of glafs, and the happy com-
bination of two or more glaiTes, which we denomi-
nate lenfes. Dioptricks is the fcience that unfolds the
principles on which fuch inftruments are conftrucled,
and the ufes to which they are applied, and you will
pleafe
283 ON DIOPTRICKS.
pleafe to recoiled that it turns chiefly on the direc-
tion which rays of light take on pafling through
tranfparent mediums of a different quality ; on pall-
ing, for example, from air into glafs or water, and
reciprocally from glafs or water into air.
As long as the rays are propagated through the
lame medium, fay air, they preferve the fame di-
rection, in the ftraight lines LA, LB, L C, LD,
(jtlate IV. fig, 2.) drawn from the luminous point L,
whence thefe rays proceed, and when they any where
meet an eye, as at fea, they enter into it, and there
paint an image of the object from which they pro-
ceeded. In this cafe the vilion is denominated fimple,
or natural ; and reprefents to us the objects as they
really are. The fcience, which explains to us the
principles of this vifion, is termed optics.
But when the rays, before they enter into the eye,
are reflected on a finely polifhed furface, fuch as a
mirror, the vifion is no longer natural ; as in this
cafe we fee the objects differently, and in a different
place, from what they really are. The fcience which
explains the phenomena prefented to us by this vi-
fion from reflected rays, is termed catoptricks. It too
iupplies us with inftruments calculated to extend the
fphere of our vifion, and you are acquainted with
fuch forts of inftruments, which, by means of one
or two mirrors, render us the fame fervices as thofe
conftructed with lenfes. Thefe are what we properly
denominate tele/copes : but in order to diftinguifh
them from the common perfpectives, which are com
poled only of glafles, it would be better to call, the
catoptrick
:
ON DIOPTRICKS. 289
catoptrick reflecting telefcopes. This mode of ex-
preilion would at leaft be more accurate ; for the
word telefcope was in ufe before the difcovery of re-
flecting inftruments, and then meant the fame thing
with perfpective.
I propofe, at prefent, to confine myfelf entirely
to dioptrical inftruments, of which we have two
forts, telefcopes or perfpeclives, and microfcopes.
In the conftruction of both we employ glafies formed
after different manners, the various forts of which
I am going to explain. They are principally three,
according to the figure given to the furface of the
glafs.
The firft is the plane, when the furface of a glafs is
plane on both fides, as that of a common mirror. If
you were to take, for example, a piece of looking-
glafs, and to feparate from it the quick-filver which
adheres to it's farther furface, you would have a glafs
both of whofe furfaces are plane, and of the fame
thicknefs throughout.
The fecond is the convex : a glafs of this denomi-
nation is more raifed in the middle than toward the
edge.
The third is the concave : fuch a glafs is- hollow
toward the middle, and rifes toward the edge.
Of thefe three different figures, which may be
given to the furface of a glafs, are produced the fix
fpecies of glaffes reprefented in fig. 1 2.
I. The piano -plane glafs has both it's furfaces
plane.
Vol. II. XJ II. The
2^0 DIFFERENCE OF LENSES.
II. The plano-convex glafs has one furface plane and
the other convex.
III. The plano-concave has one furface plane and
the other concave.
IV. The convexo-convex , or double convex ', has both
furfaces convex.
V. The convexo-concave, or menifcus, has one fur-
face convex and the other concave.
VI. Finally, the concavo-concave, or double concave,
has both furfaces concave.
It is proper to remark that the figure reprefents
the cut of thefe glaffes or lenfes.
2th- December, 176 1.
LETTER LXXIII.
Difference of Lenfes with refpecl to the Curve of their
Surfaces. Difkribution of Lenfes into Three Claffes.
FROM what I have faid refpe&ing the convex
and concave furfaces of lenfes, you will eafily .
comprehend that their form may be varied without
end, according as the convexity and concavity are
greater or lefs. There is only one fpecies of plane
furfaces ; becaufe a furface can be plane in one man-
ner only ; but a convex furface may be confidered
as making part of a fphere, and, according as the
radius or diameter of that fphere is greater or lefs,
the convexity will differ ; and as we reprefent lenfes
on paper by fegments of a circle, according as thefe
circles are greater or lefs, the form of lenfes muft be
infinite
"ralJT.
J3 late JV
E
; :■
E
Jl
B
/
\
b x M
m a ;-0
ij;',\
a IN"
S *k ¥
B
\
)
A
DIFFERENCE OF LENSES. 20. I
Infinite with refpoct both to the convexity and con-
cavity of their furfaces.
As to the manner of forming and polifhing glalP*:,
all poffible care is taken to render their figure ex-
actly circular or fpherical ; for this purpofe we em-
ploy bafons of metal formed by the turning ma-
chine, on a fpherical furface, both inwardly and
outwardly.
Let AEBDFC {plate IV. fg. 13.) be the form
of fuch a bafon, which fhall have two furfaces AEB
and CFD, each of which may have it's feparate ra-
dius ; when a piece of glafs is rubbed on the concave
fide of the bafon AEB, it will become convex ; but
if it is rubbed on the convex fide CFD, it will be-
come concave. Sand is, at firft, ufed in rubbing
the glafs on the bafon, till it has acquired the form,
and after that, a fine fpecies of earth, to give it the
laft polilh.
In order to know the real figure of the furfaces
of a lens, you have only to meafure the radius of the
furface of the bafon, on which that lens was formed ;
for the true meafure of the convexity and concavity
of furfaces, is the radius of the circle or fphere which
correfponds to them, and of which they make a part.
Thus, when it is faid, that the radius of the con-
vex furface AEB {plate V. fg. 1.) is three inches,
the meaning is, that AEB is an arch of a circle de-
fcribed with a radius of three inches, the other fur-
face AIjS being plane.
That I may convey a flill clearer idea of the dif-
ference of convexities, when their radii are greater
U 2 or
202 DIFFERENCE OF UENSE'S.-
or lefs, I ihall here pfeient you with feveral figures-*
of different convexity; (fee plate V. jig. 1.)
From this you fee, that the fmaller the radius is,,
the greater is the curve of the furface, or the greater,
it's difference from the plane"; on the contrary, the
greater the radius is, the more the furface approaches
to a plane, or the arch of the circle to a ftraight line-
If the radius were made ftill greater, the curve would
at length become hardly perceptible. You fcarcely
perceive it in the arch MN, (Jig. 2.) the radius of
which is fix inches, or half a foot ; and if the radius
were ftill extended to ten or a hundred times the
magnitude, the curve would become altogether im-
perceptible to the eye.
But this is by no means the cafeas todioptricks y.
and I fhall afterwards demonflrate, that though the
radius were a hundred or a thoufand feet, and the
curve of the lens abfolutely imperceptible, the effed
would neverthelefs be abundantly apparent. The
radius muft indeed be inconceivably great, to pro-
duce a furface perfectly plane : from which you may
conclude,,, that a plane furface might be confidered
as a convex, furface whofe radius is infinitely great,,
or as a concave of a radius infinitely great. Here it
is that convexity and concavity are confounded, fo
that the plane furface is the medium which feparates >
convexity from concavity. But the fmaller the ra-
dii are, the greater and more perceptible do -the. con-
vexities and concavities become ; and hence, we fay;
reciprocally, that a convexity or. concavity is greater.'
in.
I'
DIFFERENCE OF LENSES. 293
:in proportion as it's radius, which is the meafurc of
•it, is fmaller.
However great, in other refpects, may be the va-
riety we meet with in lenfes or glalfes, according as
their furfaces are plane, convex, or concave, and
this in an infinity of different manners; neverthe-
lefs, with refpect to the effect refulting from them in
.dioptricks, they may be reduced to the three follow-
in o; claffes :
The firft comprehends glalfes which are every
where of an equal thicknefs; whether their two fur-
-faces be plane and parallel to each other, (fig. 3.) or
the one convex and' the other concave, but con-
centric, or defcribed round the fame centre (fig. 4.)
.fo that the thicknefs fhall remain every where the
fame. It is to be remarked refpecting glalfes of this
clafs, that they produce no change in the appearance
-of the objects which we view through them ; the
objects appear exactly the fame as if nothing .intcr-
pofed ; accordingly, they are of no manner of ufe
in dioptricks. This is not becaufe the rays which
enter into thefe glalfes undergo no refraction, but
becaufe the refraction at the entrance is perfectly
ftraightened on going off, fo that the rays, after
having paffed through the glafs, refume the fame di-
rection which they had purfued before they reached
it. Glaffes, therefore, of the other two claffes, on
account of the effect which they produce, constitute
the principal object of dioptricks.
The feccnd clafs of lenfes contains thofe which are
thicker at the middle than at the edge, (Jig. 5.)
U 3 Their
294 EFFECT OF
Their effect is the fame, as long as the excefs of
the thicknefs of the middle over that of the edge has
the fame relation to the magnitude of the lens. All
lenfes of this clafs are commonly denominated convex,
as convexity predominates, though otherways one
of their furfaces may be plain, and even concave.
The third clafs contains all thofe lenfes which are
thicker at the edge than in the middle (plate V.fg. 6. J
which all produce a fimilar effect, depending on the
excefs of thicknefs toward the edge, over that in the
middle. As concavity prevails ir all fuch lenfes,
they are {imply denominated concave. They muft
be carefully diftinguifhed from thofe of the fecond
clafs, which are the convex.
Lenfes of thefe two laft claffes are to be the fubject
of my following "letters, in which I mall endeavour
to explain their effects in dioptricks.
1 2 th December, 1 761.
LETTER LXXIV,
Effect of Convex Lenfes,
N order to explain the effect produced by both
convex and concave lenfes, in the appearance of
objects, two cafes muft be diftinguimed, the one
when the object is very far diftant from the lens, and
the other when it js nearer.
But before I enter on the explanation of this, I
muft fay a few words on what is called the axis of
the lens. As the two furfaces are represented by
fegments
CONVEX LENSES. 295
fegments of a circle, you have only to draw a ftraigh t
line through the centres of the two circles ; this line
is named tlie axis of the lens. In Jig. 7 . plate V. the
centre of the arch A E B being at C, and that <jf the
arch A F B at D, the ftraight line C D is denomi-
nated the axis of the lens 'A B, and it is eafy to ice
that this axis paffes through the middle of it. The
fame thing would apply, if the furfaces of the lens
were concave. But, if one is plane, the axis will be
perpendicular to it, palling through the centre of the
other furface.
Hence it is obvious, that the axis pafies through
the two furfaces perpendicularly, and that accord-
ingly, a ray of light coming in the direction of the
axis, will fuffer no refraction, becaufe rays pailing
from one medium into another are not broken or
refracted, except when they do not enter in a per-
pendicular direction.
It may likewife be proved that all other rays paffing
through the middle of the lens O, undergo no re-
fraction, or rather that they again become parallel to
themfelves.
It muft be confidered, in order to comprehend the
reafon of this, that at the points E and F the two
furfaces of the lens are parallel to each other, for the
angle M E B, which the ray M E makes with the
arch of the circle E B, or it's tangent at E, is per-
fectly equal to the angle P F A, which this fame ray
produced, F P, makes with the arch of the circle
A F, or it's tangent at F ; you recollect that .two
U 4 ' fucii
296 EFFECT OF ;
fuch angles are denominated alternate, and that it is
demonstrated, when the alternate angles are equal,
that the ftraight lines are parallel to each other : con-
feqnently the two tangents a,t E and at F will be pa-
parallel, and it will be the fame thing as if the ray
MEFP paffed through a lens whofe two furfaces
were parallel to each other. Now, we have already
feen that rays do not change their direction in paf-
ling through fuch a lens.
Having made thefe remarks, let us now confider
a convex lens A B (plate V.Jig. 8.) whcfe axis mall
be the ftraight line O E F P, and let us fuppofe that
there is in this line, at a great diftance from the lens,
an object or luminous point O, which diffufes rays
in all directions ; forne of thefe will pafs through our
lens A B, fuch as O M, O E, and ON; of which
that in the middle O E will undergo no refraction,
but will continue it's direction through the lens in
the fame produced ftraight line F I P. The other
two rays O M and O N, in pafling through the lens
toward the edge, will be refracted, both at entering
and departing, fo that they will fomewhere meet the
axiss fay at I, and afterwards continue their progrefs
in the directions I O and I R. It might likewife be
demonftrated that all the rays which fall between M
and N will be refracted, fo as to meet with the axis
in the fame point I. Therefore the rays which, had
no lens interpofed, would have purfued their recti-
lineal direction O M and O N, will, after the refrac-
tion, p'urfue other directions, as if they had taken
their
CONVEX LENSES. 297
their departure from the point I : and if there were
an eye fomewhere at P, it would be affected juft as
if the luminous point were actually at I, though there
be no reality in this. You have only to fuppofe for
a moment, that there is at I a real object, which, dif-
fufing ' it's rays, would be equally feen by an eye
placed at P, as" It now fees the object at O by means
of the rays refracted by the lens, becaufe there is at
I an image of the object O, and the lens A B there
reprefents the object O, or tranfports it nearly to I.
The point O is therefore no longer the object of
vifion, but rather it's image, reprefented at I ; for
this is now it's immediate object.
This lens, then, produces a very confiderable
change : an object very remote O is fuddenly tranf-
ported to I, from which the eye muft undoubtedly
receive a very different impreflion from what it would
do, if, withdrawing the lens, it were to view the ob-
ject O immediately. Let O be confidered as a ftar,
the point O being fuppofed extremely diftant, the
lens will reprefent at I the image of that ftar, but an
image which it is impossible to touch, and which has
no reality, as nothing exifts at I, unlefs it be that the
rays proceeding from the point O are collected there
by the refraction of the lens. Neither is it to be
imagined, that the ftar would appear to us in the
fame manner as if it really exifted at I. How could
a body, many thoufands of times bigger than the
earth, exift at a point I ? Our fenfes would be very
differently ftru-ck by it : We muft carefully remark,
then, that an image only is i;epreientcd at I, like that
of
298 DISTANCE OF THE
of a ftar reprefented in the bottom of the eye, or
that which we fee in a mirror, the effect, of which
has nothing to furprize.
iyb December, 1 761.
LETTER LXXV.
The fame Subjecl : Dijlance of the Focus of Convex
Lenfes.
T MEAN to employ this letter in exploring the ef-
■*■ feci produced by convex lenfes, that is, fuch as
are thicker at the middle than at the edge. The
whole conlifts in determining the change which rays
undergo in their progrefs, on paffing through fuch a
glafs. In order to place this fubject. in it's cleareil
light, two cafes muft be carefully diftinguiihed, the
one, when the object is very diftant from the lens ;
and the other when it is at no great diftance. I be-
gin with confidering the firft cafe, that is, when the
object is extremely remote from the lens.
In fig. 9. of plate V. M N is the convex lens, and
the ftraight line O A B I S k's axis, paffing perpendi-
cularly through' the middle. I remark, by the way,
that this property of the axis of every lens, that of
palling perpendicularly through it's middle, conveys
thejufteft idea of it that we are capable of forming.
Let us now conceive that on this axis there is fome-
where at O an object. O P, which I here reprefent z$
a ftraight line, whatever figure it may really have ;
and as every point of this object, emits it's rays in all
directions*
FOCUS OF CONVEX LENSES. 299
directions, we confine our attention to thofe which
fall on the lens. ■ ,
My remarks fhall be at prefent farther limited to
the rays iffuing from the point O, fituated in the
very axis of the lens. The figure reprefents three
of thefe rays, O A, O M and O N, the firft of which,
O A, palling through the middle of the lens, under-
goes no change of direction, but proceeds, after hav-
ing palled through the lens, in the fame ftraight line
BIS, that is in the axis of the lens ; but the other
two rays, O M and O N, undergo a refraction both
on entering into the glafs, and leaving it, by which
they are turned alide from their firft direction, fo as
to meet fomewhere at I with the axis, from which
they will proceed in their new direction, in the
ftraight lines M I Q and N I R ; fo that afterwards,
when they fhall meet an eye, they will produce in it
the fame effect as if the point O exifted at I, as they
preferve the fame direction. For this reafon, the con-
vex lens is faid to tranfport the object O to I; but
in order to diftinguifh this point I from the real point
O, the former is called the image of the latter, which
in it's turn is denominated the object.
This point I is very remarkable, and when the ob-
ject O is extremely diftant, the image of it is like-
wife denominated the focus of the lens, of which I
fhall explain the reafon. If the fun be the object at
0, the rays which fall on the lens are all collected at
1, and being endowed with the quality of heating, it
is natural that the concourfe of fo many rays at I,
fhould produce a degree of heat, capable of fetting
on
300 DISTANCE OF THE
on fire any combuftible matter that may be placed
there. Now, the place where fo much heat is col-
lected we call the focus ; the reafon of this denomi-
nation with refpect. to convex lenfes is evident.
Hence, too, a convex lens is denominated a burning-
glafs, the effects of which you are undoubtedly well
acquainted with. I only remark that this property
of collecting the rays of the fun, in a certain point
called their focus, is common to all convex lenfes,;
they likewife collect the rays of the moon, of the
itars, and of all very diftant bodies; though their
force is too fmall to produce any heat, we neverthe-
lefs employ the fame term, focus ; the focus of a
glafs, accordingly, is nothing elfe but the fpot where
the image of very diftant objects is reprefented: to
which this condition mult ftill be added, that the ob-
ject ought to be fituatedin the very axis of the lens ;
for if it be out of the axis, it's image will likewife
be reprefented out of the axis : I fliall have occauon
to fpeak of this afterward, -
It may be proper, ftill farther, to fubjoin the fol-
lowing remarks refpecting the focus :
i. As the point O, or the object, is infinitely dif-
tant, the rays O M, O A, and O N, may be confi-
dcred as parallel to each other, and, for the fame
•reafon, parallel to the axis of the lens.
2. The focus I, therefore, is the point behind the
vglafs, where the rays parallel to the axis, whicli falls
'On the lens, are collected by the refraction of the,
^ens.
3. The fogAS of a lens, and . the fpot where the
image
FOCUS OF CONVEX LENSES. . Jfif
image of an object, infinitely diftant, and fituated in
the axis of the lens, is reprefented, are the fame
thing.
4. The diftance of the point I behind the lens,
that is the length of the line B I, is called the dif-
tance of the focus of the lens. Some authors call it
the focal diftance.
5. Every convex lens has it's particular diftance of
focus, one greater, another lefs, which is eafily afcer-
tained by expofing the lens to the fun, and obferving
where the rays meet.
6. Lenfes- formed by arches of fmall circles, have
their focufes very near behind them; but thofewhofe
furfaces are arches of great circles, have more diftant
focufes.
7. It is of importance to know the focal diftance
of every convex lens employed in dioptricks ; and it
is fufficient to know the focus in order to form a judg-
ment of all the effects to be expected from it, whether
in the conftruction of telefcopes or microfcopes.
8. If we employ lenfes equally convex on both
fides, fo that each furface fhall correfpond to the
fame circle ; then the radius of that circle gives
nearly the. focal diftance of that lens: thus, to make
a burning -glafs which fhall burn at the diftance of su
foot, you have only to form the two furfaces arches
of a circle whofe radius is one foot.
9. But when the lens is plano-convex, it's focal;
diftance is nearly equal to the diameter of the circle,
which... correfponds to the convex furface.
Acquaintance-
302 DISTANCE OF THE
Acquaintance with thefe terms will facilitate the
knowledge of what I have farther to advance on thi*
fubject.
1 9/(6 December j 176 1.
LETTER LXXVL
Diftance of the Image ofObjecls.
HAVING remarked that an object infinitely
diftant, is reprefented by a convex lens in the
very focus, provided fuch object be in the axis of
the lens, I proceed to nearer objects, but always fitu-
ated in the axis of the glafs ; and I obferve, firft, that
the nearer the object approaches to the lens, the far-
ther the image retires.
Let us accordingly fuppofe that F {plate V.fig. 10.)
is the focus of the lens MM, fo that an object in-
finitely diftant before the glafs, or at the top of the
figure, the image fhall be reprefented at F ; on bring-
ing the object nearer to the glafs, and placing it fuc-
ceflively at P Q R, the image will be reprefented at
the point p q r, more diftant from the lens than the
focus : in other words, if A P is the diftance of the
object, Bp will be the diftance of the image, and if
A O is the diftance of the object, B q will be that of
the image, and the diftance Br of the image will
correfpond to the diftance A R of the object*
There is a rule by which it is eafy to calculate the
diftance of the image behind the lens, for every dif-
tance
IMAGE OF OBJECTS.
3°3
tance of the object before it, but J will not tire you
with a dry expofition of this rule ; it will be fufficient
to remark, in general, that the more the diftance of
the object before the glafs is diminifhed, the more is
the diftance of the image behind it increafed. I ihall
to this fubjoin the inftance of a convex lens, whofe
focal diftance is 6 inches, or of a lens fo formed, that
if the diftance of the object is infinitely great, the
diftance of the image behind the lens fhall be precifely
fix inches; now, on bringing the object nearer to the
lens, the image will retire, according to the grada-
tions marked in the following table :
Diftance of the Objecl.
Infinity
6
42
7
24
8
18
9
*.5
10
12
12
10
*5
9
18
8
24
7
42'
6
Infinity".
Diftance of the Ima^e.
Thus the object being 42 inches diftant from the lens,
the image will fall at the diftance of 7 inches, that is
one inch beyond the focus. If the object is at the
diftance of 24 inches, the image will be removed to
the diftance of 8 inches from the lens, that, is two
inches beyond the focus, and fo of the reft;
Thoueh
304 DISTANCE OF THE
Though thefe numbers are applicable only to a
lens, whofe focal diftance is 6 inches, fome general
confequences may, however, be deduced from them.
1. If the diftance of the object is infinitely great,
the image falls exadtly in the focus.
2. If the diftance of the object is double the dif-
tance of the focus, the diftance of the image will like-
i wife be double the diftance of the .focus ; in other
words, the objeft and the image will be equally diftant
from the lens. In the example above exhibited, the
diftance of the object being 12 inches, that of the
image is likewife 1 2 inches. -
3. When the object is brought fo near the lens,
that the diftance is precifely equal to that of the
focus, fay 6 inches, as in the preceding example, then
the image retires to an infinite diftance behind the
lens.
4. It is likewife obfervable in general, that the dif-
tance of the object and that of the image reciprocally
correfpond, or, if you put the object in the place of
the image, it will fall in the place of the object.
5. If, therefore, the lens MM (plate V. fig. 11. )
collects at I the rays which iffue from the point O,
that fame lens will likewife there collect rays iifuing.
from the point I. . ,
6. It is the confequence of a great principle in-diop-
tricks, in virtue of which it may be maintained, that
whatever are the refractions which rays have under-
gone in palling through feveral refringent mediums,
they may always return in the fame direction.
This truth is of much importance in the know-
2 ledge
IMAGE OF OBJECTS. $0$
ledge of lenfes : thus when I know, for example, that
a lens has reprefented, at the diftance of 8 inches, the
image of an object 24 inches diftant, I may confi-
dently infer, that if the object were 8 inches diftant,
the fame lens would reprefent it's image at the dif-
tance of 24 inches.
It is farther eflential to remark, that when the dif-
tance of the object is equal to that of the focus, the
image will fuddenly retire to an infinite diftance ;
which perfectly harmonizes with the relation exifting
between the object and the image.
You will no doubt be curious to know in what
place the image will be reprefented when the object
is brought ftill nearer to the lens, fo that it's diftance
fhall become lefs than that of the focus. This quef-
tion is the more embarrafling, that the anfwJr muft
be, the diftance of the image will, in this cafe, be
greater than infinity, fince the nearer the object ap-
proaches the lens, the farther does the image retire.
But the image being already infinitely diftant, how
is it poflible that diftance mould be increafed ? The
queftion might undoubtedly puzzle philofophers, but
is of eafy folution to the mathematician. The image
will pafs from an infinite diftance, to the other fide
of the lens, and confequently will be on the fame fide
with the object. However ftrange this anfwer may
appear, it is confirmed, not only by reafoning, but
by experience, fo that it is impofiible to doubt of it's
folidity ; to increafe beyond infinity is the fame thing
with patting to the other fide : this is unqueftionably
a real paradox.
lAd D-ectiinher, 1761.
Vol. 1L X LETTER
$o6 MAGNITUDE OF IMAGES.
LETTER LXXVII.
Magnitude of Images.
YOU can no longer doubt that every convex lens
muft reprefent fomewhere the image of an
object prefented to it ; and that, in every cafe, the
place of the image varies as much, according to the
diftance of the object, as according to the focal dis-
tance ,of the lens : but a very important article re-
mains yet to be explained, I mean the magnitude of
the image.
When fuch'-a lens reprefents to us the image of
the fun, of the moon, or of a ftar, at the diftance of
a foot, you are abundantly fenfible that thefe images
muft be incomparably fmaller than the objects them-
felves. A ftar being much greater than the whole
earth, how is it poffible that an image of fuch mag-
nitude fhould be reprefented to us at the diftance of
a foot ? But the ftar appearing to us only as a point,
the image, reprefented by the lens, likewife refembles
a point, and, confequently, is infinitely fmaller than
the objecl itfelf.
There are then, in every reprefentation made by
lenfes, two things to be confidered; the one refpects
the place where the image is reprefented, and the
other, the real magnitude of the image, which may
be very different from that of the objecl:. The firft
being Sufficiently elucidated, I proceed to furniftiyou
with a very fimple rule, by. which you will be en-
abled, in every cafe, to determine what muft be. the ,
magnitude of the image reprefented by the lens.
Let
~Vour.
f/afrV
^PiA/oTncb&r
Fi<j.l.
Third of ariJrich-
JFiftA ofanlrvch-
JZiyAiA <7fan.Jn*A
I>y.6
:M<
»>r
S IL rT
MAGNITUDE OF IMAGES. 307
Let O P (plate VI. jig. 1 . ) be any object whatever,
iituated on the axis of the convex lens M N ; we
mull firft look for the place of the image, which is
at I, fo that the point I mall be the reprefentation of
the extremity O of the object, as the rays iffuing
from the point O are there collected by the refraction
of the lens. Let us now fee in what place will be re-
prefented the other extremity P of the object ; for
this purpofe, let us confider the rays P M, P A, P N,
which, iiTuing from the point P, fail on the lens ; I
obferve that the ray P A, which pafles through the
middle of the lens, does not change it's direction,
but continues it's progrefs in the ftraight line AKS;
it will be, therefore, fomewhere in this line at K, that
the other rays P M and P N will meet : in other
words, the point K will be the image of the other
extremity P of the object, the point I being that of
the extremity O : hence it is eafy to conclude that
I K will be the image of the object O P, reprefented
by the lens.
In order then, to determine the magnitude of this
image, having found the place I, you have only to
draw from the extremity P of the object, through A,
the middle of the lens, the ftraight line P A K S, and
to raife from I the line I K perpendicular to the axis,
and this line I K will be the image in queftion ; it is
evident from this that the image is reverfed, fo that
if the line O R were horizontal, and the object O P
a man, the image would have the head Kundermoft,
and the feet I upward.
On this I fubjoin the following remarks :
X 2 1. The
3'o8 MAGNITUDE OF IMAGES.
i. The nearer the image {plate VI. fig. 2.) is to the
lens, the fmaller it is ; and, the more remote it is,
the greater it's magnitude. Thus O P being the ob-
ject placed on the axis before the lens M N, if the
image fell at O it would be fmaller than if it fell at
R, S, or T. For, as the ftraight line PA/, drawn
from the fummit of the object P, through the middle
of the lens, always terminates the image at whatever
diftance it may be, it is evident, that among the lines
Q q, R r, S s, T t, the firft Q q is the fmalleft, and
that the others increafe in proportion as they remove
from the lens.
1. There is one cafe in which the image is precifely
equal to the object : it is when the diftance of the
image is equal to that of the object ; and this takes
place, as I have already remarked, when the diftance
of the object A O is double that of the focus of the
lens ; the image will then be T /, fo that the diftance
B / is equal to A O. You have only then to confider
the two triangles OAP and T At, which having,
the oppofite angles at the point A, as well as the
lides A O and A T equal each to each, as likewife the
angles at O and T, which are both right angles : thefe
two triangles will be every way equal, and confe-
quently the fide T /, which is the image, will be equal'
to the fide O P, which is the object.
3. If the image were twice farther from the lens
than the object, it would be double the object ; and,
in general, as many times as the image is farther from
the lens than the object, fo many times will it be
greater than the object. For the nearer you bring
the
MAGNITUDE OF IMAGES. . 309
the object to the glafs, the farther the image retires,
and confequently the greater it becomes.
4. The contrary takes place when the image is
nearer the lens than the object ; it is then as many
times fmaller than the object., as it is nearer the lens
than the object is. If then the diftance of the image
were one thoufand times lefs than that of the object,
it would likewife be one thoufand times fmaller.
5. Let us apply this to burning-glaffes, which, being
expofed to the fun, reprefent it's image in the focus,
or rather reprefent the focus, that is, the luminous
and brilliant circle which burns, and which is nothing
elfe but the image of the fun reprefented by the lens.
You will no longer be furprized, then, at the fmall-
nefs of the image, notwithstanding the prodigious
magnitude of the fun, it being as many times fmaller
in the focus than the real fun, as the diftance of the
fun from the lens is greater than that of the image,
6. Hence likewife it is evident, that the greater is
the diftance of the focus of a burning-glafs, the more
brilliant alfo is the circle in the focus, that is, the
greater will be the image of the fun : and the dia,
meter of the focus is always about one hundred times
fmaller than the diftance of the focus from the lens,
I {hall afterwards explain the different ufes which
may be made of convex lenfes ; they are all fuffi-
ciently curious to merit attention.
26th December, 1761.
LETTER
31® BURNING GLASSES.
LETTER LXXVIII.
Burning Glaffes.
r § ^HE firft ufe of convex lenfes, is their employ.
,-*- ment as burning-glafTes, the effed of which
mull appear altogether altonilhing, even to thofe who
already have fome acquaintance with natural philo-
fophy. In fact, who could believe, that the image
of the fun, limply, Ihould be capable of exciting fuch
a prodigious degree of heat ? But your furprize will
ceafe, if you pleafe to pay fome attention to the fol-
lowing reflections.
i. Let MN, (plate VI. Jig. 3.) be a burning-glafs,
which receives on it's furface the rays of the fun
R, R, R, refracted in fuch a manner as to prefent at
F a fmall luminous circle, which is the image of the
fun, and fo much fmaller as it is nearer to the glafs.
2. All the rays of the fun, which fall on the fur-
face of the glafs, are collected in the fmall fpace of
the focus F; their effect:, accordingly, muft, in that
fpace, be as many times greater as the furface of the
glafs exceeds the magnitude of the focus, or of the
fun's image. We fay that the rays, which were dif-
perfed over the whole furface of the glafs, are con-
centrated in the fmall fpace F.
3. The rays of the fun having a certain degree of
heat, they exert their power, in a very fenlible man-
ner, at the focus ; it is poflible even to calculate how
many times the heat at the focus mull exceed the
natural
BURNING GLASSES. 3H
natural heat of the fun's rays: we have only to
obferve how many times the furface of the glafs is
greater than the focus.
4. If the glafs were not greater than the focus, the
heat would not be ftronger at the focus than any
where elfe ; hence we muft conclude, that in order
to the production of a ftrong heat by a burning-
glafs, it is not fufficient that it mould be convex, or
that it mould reprefent the image of the fun, it muft,
betides, have a furface which feveral times exceeds
the magnitude of the focus, which is fmaller in pro-
portion as it is nearer to the glafs.
5. France is in poffeflion of the moft excellent burn-
ing-glafs ; it is three feet in diameter, and it's furface
is calculated to be nearly two thoufand times greater
than the focus, or the image of the fun which it re-
prefents. It muft produce, therefore, in the focus, a
heat two thoufand times greater than that which we
feel from the fun. It's effects are, accordingly, pro-
digious : wood of every kind is, in a moment, fet on
fire ; metals are melted in a few minutes ; and, in
general, the moft ardent fire which we are capable
of producing, is not once to be compared with the
vehement heat of this focus,
6. The heat of boiling water is calculated to be
about thrice greater than what we feel from the rays
of the fun in fummer, or, which amounts to the
fame thing, the heat of boiling water is thrice greater
than the natural heat q( the blood in the human body.
But in order to melt lead, we muft have a heat thrice
greater than is requiiite to make water boil ; and to
X 4 melt
312 ■ BURNING GLASSES.
melt copper a heat ftill thrice greater is neceffary.
To melt gold requires a much higher degree of heat.
Heat, then, one hundred times greater than that of
our blood is capable of melting gold ; how far then
mull a heat two thoufand times greater exceed the
force of our ordinary fires ?
7. But how are thefe prodigious effects produced
by the rays of the fun collected in the focus of a
burning-glafs ? This is a very difficult queftion, with
refpect to which philofophers are very much divided.
Thofe who maintain that the rays are an emanation
from the fun, darted with the amazing velocity which
I formerly defcribed, are not greatly embarraffed for
a folution ; they have only to fay that the matter of
the rays, linking bodies with violence, muft totally
break and deflroy their minute particles. But this
opinion is no longer admitted m found philofophy.
S. The other fyftem, which makes the nature of
light; to confift in the agitation of the ether, appears
little adapted to explain thefe furprizing effects of
burning-glaffes. On carefully examining, however,
all the circumftances, we fhall foon be convinced of
the poffibility of this. The natural rays of the fun,
as they fall on bodies, excite the minute particles of
the furface, to a concuflion, or motion of vibration,
which, in it's turn, is capable of exciting new rays,
and by thefe the body in queftion is rendered vifible.
And a body is illuminated only [q far as thefe proper
particles are put into a motion of vibration fo rapid
as to be capable of producing new rays in the ether,,
9. It is clear, then, that if the natural rays of the
fun
THE CAMERA ODSCURA. 313
fun have fufficicnt force to agitate the minute par-
ticles of bodies, thofe which are collected in the focus
mult put the particles which they meet there into
an agitation lb violent, that their mutual adhefion is
entirely difiblved, and the body itfclf completely de-
ftroyed, which is the effect of fire. For if the body
is combuftible, as wood, the diffolution of thefe mi-
nute particles, joined to the rhoft rapid agitation,
makes a confiderable part of it to fly off into air, in
the form of fmoke, and the groffer particles remain
in form of allies. Fufible bodies, as metals, become
liquid by the diffolution of their particles, whence we
may comprehend how fire acts on bodies ; it is only
the adhefion of their minuteft particles which is at-
tacked, and the particles themfelves are thereby after-
wards put into the molt violent agitation. Here,
then, is a very ftriking effect of burning-glaffes, which
derives its origin from the nature of convex lenfes,
There are befides many other wonderful effects to be
defcribed.
2 StI? December, 1761.
LETTER LXXIX.
The Camera Obfcura.
WE likewife employ convex lenfes in the ca-
mera obfcura, and by means of them, all ex-
ternal objects are prefented in the darkened room on
a white furface, in their natural colours, in fuch a
manner that landfcapes and public buildings, or ob-
jects
314 THE CAMERA OBSCURA.
jects in general, are reprefented in much greater per-
fection than the power of the pencil is capable of
producing. - Painters accordingly avail themfelves of
this method, in order to draw, with exactnefs, land-
fcapes and other objects which are viewed at a dif-
tance. The camera obfcura, then, is to be the fubject
of this letter.
E F G H, {plate VI. fig. 4.) reprefents the form of a
camera obfcura, clofely fhut up on all fides, except one
little round aperture made in one of the window
mutters, in which is fixed a convex lens, of fuch a
focus as to throw the image of external objects, fay
the tree O P, exactly on the oppofite wall F G, at 0 p.
A white and moveable table is likewife employed,
which is put in the place of the images reprefented.
The rays of light, therefore, can be admitted into
the chamber only through the aperture M N, in
which the lens is fixed, without which total darknefs
would prevail.
Let us now confider the point P of any object,
fay the item of our tree OP. It's rays PM, PA,
P N will fall, then, on the lens M N, and be refracted
by it, fo as to meet again at the point p on the wall,
or on a white table placed there for the purpofe.
This point p will confequently receive no other rays
but fuch as proceed from the point P ; and in like
manner every other point of the table will receive
only the rays which proceed from the correfponding
point of the object ; and reciprocally, to every point
of the external object will correfpond a point on the
table, which receives thofe rays and no other. If the
lens
THE CAMERA OBSCURA. 315
lens were to be removed from the aperture M N, the
table would be illuminated in quite a different man-
ner, for in that cafe every point of the object would
diffufe it's rays over the whole table, fo that every
point of the table would be illuminated at once by
all the external objects, whereas at prefent it is fo by
one only, that whofe rays it receives j from this you
will eafily comprehend that the effecl: muft be quite
different from what it would be if the rays entered
fimply by the aperture MN into the chamber.
Let us now examine, fomewhat more clofely,
wherein this difference confifts ; and let us firft fup-
pofe that the point P of the object is green, the point
of the table p will, therefore, receive only thofe green
rays of the object P, and thefe, re-uniting on the
wall or table, will make a certain impreflion, which
here merits confideration. For this purpofe you will
pleafe to recoiled the following propofitions which I
had formerly the honour of explaining to you.
1. Colours differ from each other in the fame
manner as mufical founds : each colour is produced
by a determinate number of vibrations, which, in a
given time, are excited in the ether. The green
colour of our point P is accordingly appropriated
to a certain number of vibrations, and would no
longer be green were thefe vibrations more or lefs
rapid. Though we do not know the number of vi-
brations which produce fuch or fuch a colour, we
may, however, be permitted to fuppofe here that
green requires twelve thoufand vibrations in a fe-
cond, and what we affirm of this number, twelve
thoufand,
$l6 THE CAMERA OBSCURA.
thoufand, may likewife be eafily underflood of the
real number, whatever it be.
2. This being laid down, the point p on the white
table will be ftruck by a motion of vibration, of
which twelve thoufand will be completed in a fecond.
Now, I have remarked that the particles of a white
furface are all of fuch a nature as to receive every
fort of agitation, more or lefs rapid, whereas thofe
of a coloured furface are adapted to receive only
that degree of rapidity which correfponds to their
colour. And as our table is white, the point p in it
will be excited to a motion of vibration correfpond-
ing to the colour of green ; in other words it will be
agitated twelve thoufand times in a fecond.
3. As long as the point p, or the particle of the
white furface which exifts there, is agitated with a
fimilar motion, this will be communicated to the
particles of the ether which furround it ; and this
motion diffufing itfelf in all directions, will generate
rays of the fame nature, that is to fay, green ; juft as
in mufic, the found of a certain note, fay C, agitates
a firing wound up to the fame tone, and makes it
emit a found without being touched.
4. The point p of the white table will accordingly
produce green rays, as if it were dyed or painted that
colour : and what I affirm of the point p, will equally
take place with refpecl to all the points of the illu-
minated table, which will produce all the rays, each
of the fame colour with that of the object whofe
image it reprefents. Every point of the table will,
therefore,
THE CAMERA OBSCURA. 317
therefore, become vifible, under a certain colour, as
if it were actually painted that colour.
5. You will perceive, then, on the table, all the
colours of the external objects, the rays of which
will be admitted into the chamber through the lens :
each point in particular will appear of the colour of
that point of the object which correfponds to it, and
you will fee on the table a combination of various
colours, difpofed in the fame order as you fee them
in the objects themfelves, that is to fay, a reprefenta-
tion, or rather the perfect picture of all the objects
on the outfide of the dark chamber which are before
the lens NN.
6. All thefe objects will, however, appear reverfed
on the table, as you will conclude from what I have
faid in my foregoing letters. The under part of the
tree O will be reprefented at 0, and the fummit P at
p : for, in general, each object muft be reprefented,
on the white table, in the place which is the termi-
nation of the ftraight line drawn from the object P
through the middle of the lens A: that which is
upward will, confequently, be reprefented down-
ward, and that which is to the left Will be to the
right; in a word, every thing will be reverfed in
the picture ; the reprefentation will, neverthelefs, be
more exact and more perfect than the moft accurate
painter is capable of producing.
7. You will further remark, that this picture will
be fo much fmaller than the objects themfelves, in
proportion as the focus of the lens is fhorter. Lenfes
of a fhort focus will accordingly give the objects in
miniature ;
318 THE CAMERA OBSCURA.
miniature ; and if you would wifli to have them
magnified, you muft employ lenfes of a longer focus,
or which reprefent the images at a greater diftance.
8. In order to contemplate thefe reprefentations
more at eafe, the rays may be intercepted by a mir-
ror, from which they are refracted, fo as to repre-
fent the whole picture on a horizontal table ; and
this is of peculiar advantage when we wifli to copy
the images.
id January , 1762.
LETTER LXXX.
Refietllons on the Reprefent ation in the Camera Obfcura.
THOUGH you can no longer entertain any
doubt refpecting the reprefentations made in
a dark chamber, by means of a convex lens, I hope
the following reflections will not appear fuperfluous,
as they ferve to place this fubject in a clearer light.
1. The chamber muft be completely darkened, for,
were the light admitted, the white table would be
vifible, and the particles of it's furface, already agi-
tated, would be incapable of receiving the impreflion
of the rays which unite to form the images of ex-
ternal objects. Though, however, the chamber were
a little illuminated, flill fomething of the reprefenta-
tion would appear on the table, but by no means fo
vivid as if the chamber were entirely dark.
2. We muft carefully diftinguifti the picture re-
prefented on the white table, from the image which
the
THE CAMERA OBSCURA. 3I9
the lens, in virtue of it's own nature, reprefents, as I
have formerly explained. It is very true, that placing
the table in the very place where the image of the
objects is formed by the lens, this image will be con-
founded by the picture we perceive on the table ;
thefe two things are, neverthelefs^ of a nature entirely
different : the image is only a fpectre or lhade float-
ing in the air, which is vifible but in certain places,
whereas the reprefentation is a real picture, which
every one in the chamber may fee, and to which du-
ration alone is wanting.
3. In order the more clearly to elucidate this dif-
ference, you have only to confider carefully the na-
ture of the image o, (plate VI. fig. 5.) reprefented by
the convex lens M N, the object being at O. This
image is nothing elfe but the place in which the rays
OM, OC, ON of the object, after having paffed
through the lens, meet by refraction, and thence
continue their direction as if they proceeded from
the point 0, though they really originated from O,
and by no means from 0.
4. Hence the image is vifible only to eyes fituated
fomewhere within the angle R 0 Q, as at S, where
an eye will actually receive the rays which come to
it from the point 0. But an eye fituated out of this
angle, as at F or V, will fee nothing at all of it, be-
caufe no one of the rays collected ate is directed to-
ward it : the image at 0, therefore, differs very efien-
tially from a real object, and is vifible only in certain
places,.
, x. But
320 THE CAMERA 0BSCURA.
5. But if a white table is placed at 0, and it's fur-
face at this point 0 is really excited to an agitation
fimilar to that which takes place in the object O, this
fpot 0 of the furface itfelf generates rays which ren-
der it vifible every where. Here, then, is the dif-
ference between the image of an object, and it's re-
prefentation made in a camera obfcura : the image
is vifible only in certain places, namely, thofe through
which are tranfmitted the rays that originally pro-
ceed from the object ; whereas the picture, or repre-
fentation formed on the white table, is feen by it's
own rays, excited by the agitation of the particles
of it's furface, and confequently vifible in every place
of the camera obfcura.
6. It is likewife evident, that the white table muft
abfolutely be placed exactly in the place of the image
formed by the lens, in order that every point of the
table may receive no other rays except fuch as pro-
ceed from a fingle point of the object : for if other
rays were likewife to fall upon it, they would dif-
turb the effect of the former, or render the repre-
fentation confufed,
7. Were the lens to be entirely removed, and free
admiffion given to the rays into the dark chamber,
the white table would be illuminated by it, but no
picture would be vifible. The rays of the different
objects would fall on every point of the table,, with-
out exprefling any one determinate image. The
picture, accordingly, which we fee in a camera ob-
fcura, on a white furface, is the effect of the convex
1 lens
THE CAMERA OESCURA. 32 t
lens fixed in the fhutter : this it is which collects
anew, in a fingle point, all the rays that proceed
from one point of the object.
8. A very lingular phenomenon is here, however,
obfervable, when the aperture, made in the window-
fliutter of the dark chamber, is very fmall: for though
no lens be applied, you may, neverthelefs, perceive
on the oppofite partition the images of external ob-
jects, and even with their natural colours : but the
reprefentation is very faint and confufed, and if
the aperture is enlarged this reprefentation entirely
difappears. I mall explain this phenomenon.
Infg. 6. plate VI. MN is the frnall aperture through
which the rays of external objects are admitted into
the dark chamber EFGH. The wall FG oppofite
to the aperture is white, the better to receive the
impremon of rays of all forts.
Let the point O be an object, of which the rays
OM, ON alone, with thofe which fall between them,
can enter into the chamber. Thefe rays will be con-
fined to the fmall fpace o o of the wall, and will illu-
minate it. This fpace o o will be fo much fmaller,
or approach the nearer to a point, *fh proportion as
the aperture MN is fmall : if then this aperture were
very fmall, we mould have the effect already, de-
fcribed, according to which every point of the white
table receives only the rays proceeding from a fingle
point of the object : there would be produced, of
co^fequence, a reprefentation iimilar to that which
is produced by the application of a convex lens to an
aperture in the window-mutter. But in the prefent
Vol. II. Y cafe,
322 OF THE MAGIC LANTERN,
cafe, the aperture being of a certain extent, every
point O of the object will illuminate a certain fmall
ipace o o on the wall, and agitate it by it's rays. The
iame thing then, nearly, would take place, as if a
painter, inftead of making points with a fine pencil,
mould with a coarfe one make fpots of a certain
magnitude, attending, however, to defign and co-
louring, the reprefentation made on the wall will
have a refemblance to this fort of daubing ; but it
will be clearer in proportion to the fmallnefs of the
aperture by which the rays are admitted.
tyh January , 1762.
LETTER LXXXI.
Of the Magic Lantern^ and Solar Micro/cope,
r I ^HE camera obfcura has properly no effect except
-** on very diftant objects, but you will ealily com-
prehend, that it's application may be equally ex-
tended to nearer objects ; for this purpofe the white
table rnuft be removed further from the lens, con-
formably to this general rule, that the nearer the
object is brought to the convex lens, the farther
does the image, where the white table ought to be
placed, retire from it ; and if the chamber is not of
fufficient depth, a different lens, of a ihorter focus,
muft be employed.
You may place then, out of the chamber, before
the. aperture to which the convex lens is fitted, any
abject or picture whatever, and you will fee a copy
of
AND SOLAR MICROSCOPE. 323
of it on the white table within the dark chamber,
greater or fmaller than the original, according as the
diftance of the image is greater or fmaller ; but it
would be more commodious, undoubtedly, if the
object, could be expofed within-fide the dark cham-
ber, in order to it's being moved and changed at
pleafure. But here a great difficulty occurs ; the
object itfelf wrould, in this cafe, be darkened, and
confequently rendered incapable of producing the
effect we wifh.
•The thing wanted, then, is, to illuminate the ob-
ject as much as poflible, within-fide the dark cham-
ber, and at the fame time to exclude the light. I
have found out the means of doing this. You will
recoiled that I conftructed a machine to the effect I
am mentioning, which I had the honour of preferr-
ing to you fix years ago ; and now you will eafily
comprehend the ftructure, and the principles on
which it is founded.
This machine confifts of a box very clofe on all
fides, nearly of a figure fimilar to fig. 7. plate VIL
The farther fide of which E G has an opening I K,
in which are to be fitted the objects, portraits or
Other pictures OP which you mean to reprefent ; on
the other fide, directly oppofite, is a tube MNQR,
containing aconvexdens MN; this tube is moveable,
for the purpofe of bringing the lens nearer to the
object, or of removing it at pleafure. Then, pro-
vided the object OP be well illuminated, the lens
will throw fomewhere the image of it op, and if
you there place a white tablet, you will fee upon it
Y 2 a perfect
324 OP THE magic lantern,
a perfect copy of the object, fo much the clearer as
the object itfelf is more illuminated.
For this purpofe I have contrived in this box two
fide wings for the reception of lamps with large
wicks, and in each wing is placed a mirror to reflect
the light of the lamps on the objects OP ; above, at
EF, is a chimney by which the fmoke of the lamps
paffes off. Such is the construction of this machine,
within which the object O P may be very ftrongly
illuminated, while the darknefs of the chamber fuf-
fers no diminution. In order to the proper ufe of
this machine, attention muft be paid to the follow-
ing remarks.
I. On Hiding inward the tube MNQR, that is
bringing the lens MN nearer toi the object O P, the
image op will retire ; the white tablet muft therefore
be removed backward, to receive the image at the
juft diftance ; the image will thereby be likewife
magnified, and you may go on to enlarge it at plea-
sure by prefTmg the lens MN nearer and nearer to
the objeft OP.
II. On removing the lens from the object, the
diftance of the image will be diminifhed : the white
tablet muft in this cafe be moved nearer to the lens,
in order to have a clear and diftinct reprefentation,
but the imas:e will be reduced.
III. It is obvious that the image will be always
reverfed ; but this inconveniency is eafily remedied ;
you have only to reverfe the object OP itfelf, turn-
ing it upfide down, and the image will be repre-
fented upright on the white tablet.
IV. It
AND SOLAR MICROSCOPE. 325
IV. It is a farther general remark, that the more
the image is magnified on the white tablet, the lefs
luminous and diflinct it will be ; but on reducing
the image, it is rendered more diftincl and brilliant.
The reafon is plain, the light proceeds wholly from
the illumination of the object ; the greater that the
fpace is, over which it is diffufed, the more it mud
be weakened, and the more contracted it is, the
more brilliant.
V. Accordingly, the more you wifh to magnify
the reprefentation, the more you muft ftrengthen
the illumination of the object, by increafing the light
of the lamps in the wings of the machine : but for
fmall reprefentations a moderate illumination is fuf-
ficient.
The machine which. I have been defcribin^ is
called the magic-lantern^ to diftinguifh it from the
common camera obfcura, employed for reprefenting
diftant objects : its figure, undoubtedly, has pro-
cured it the name of .lantern, efpecially as it is de-
figned to contain light ; but the epithet magic mufl
have been an invention of it's firft proprietors, who
wifhed to imprefs the vulgar with the idea of magic
or witchcraft. The ordinary magic-lanterns, how-
ever, are not conftructed in this manner, and ferve
to reprefent no other objects but figures painted on
glafs, whereas this machine may be applied to objects
of all forts.
It may even be employed for reprefenting the
fmaileft objects, and for magnifying the reprefenta*
tion to a prodigious fize, £o as that the fmallefl fly
Y 3 fhall
326 USE AND EFFECT OF A
ihall appear as large as an elephant : but, for this
purpofe, the ftrongeft light that lamps can give is
far from being fuiEcient ; the machine muft be dif-
pofed in fuch a manner that the objects may be illu-
minated by the rays of the fun, ftrengthened by a
burning-glafs : the machine, in this cafe, changes
it's name, and is called the folar-mkrofcope : I fhall
. have occafion to fpeak of it more at large in the
fequel.
Stb January, '1762.
LETTER LXXXII.
life and Effect of ajtmple Con-vex Lens.
'E likewife employ convex lenfes for imme-
diately looking through : but in order to
explain their different ufes, we muft go into a clofer
inveftigation of their nature.
Having obferved the focal diftance of fuch a glafs,
I have already remarked, that when the object is
very remote, it's image is reprefented in the focus
itfelf, but on bringing the object nearer to the lens,
the image retires farther and farther from it ; fo that
if the diftance of the object be equal to that of the
focus of the lens, the image is removed to* an in-
finite diftance, and, confequently, becomes infinitely
great.
The reafon is, that the rays OM, OM, (plate VI.
fig. J.J which come from the point O, are refracted
by the lens, fo as to become parallel to each other,
as
SIMPLE CONVEX LENS. 327
as NF,NF; and as parallel lines are fuppofed to pro-
ceed forward to infinity, and as the image is always
in the place where the rays, iiTuing from one point
of the object, are collected again after the refraction ;
in the cafe when the object OA is equal to that of
the focus of the lens, the place of the image removes
to an infinite diftance ; and as it is in different whe-
ther we conceive the parallel lines NF and NF to
meet at an infinite diftance to the left or to the right*
it may be faid indifferently, that the image is to the
right or to the left, infinitely diftant, the effect being
always the fame.
Having made this remark, you will eafily judge
what muft be the place of the image, when the ob-
jeci: is brought ftill nearer to the lens.
Let OP, {plate VI. fig. 8.) be the object, and as
it's diftance OA from the convex lens is lefs than
the diftance of the focus, the rays OM, OM, which
fall upon it from the point O, are too divergent to
admit of the poflibility of their being rendered pa-
rallel to each other by the refractive power of the
lens ; they will, therefore, be ftill divergent after the
refraction, as marked by the lines NF, NF, though
much lefs fo than before, therefore if thefe lines are
produced backward, they will meet fomewhere at c,
as you may fee in the dotted lines N o, N o. The
rays NF, NF, wrill, of confequence, after having
palled through the lens, preferve the fame direction
as if they had proceeded from the point o, though
they have not actually paffed through that pointy as
it is only in the lens that they have taken this new
Y 4 direction.
32b USE AND EFFECT OF A
direction. An eye which receives thefe refracted
rays NF, NF, will be, therefore, affected as if they
really came from the point o, and will imagine that
the object of it's vifion exifts at o. There will, how-
ever, be no image at that point, as in the preceding
cafe : to no purpofe would you put a white tablet at
o, it would prefent no picture there, for want of
rays ; for this reafon we fay that there is an imagi-
nary image at 0, and not a real, one : the term ima-
ginary being oppofed to that of real.
Neverthelefs, an eye placed at E receives the fame
impreilion as if the object OP, from which the rays
originally proceed, exifted at o. It is of great im-
portance, then, to know, as in the preceding cafe?,
the place and the magnitude of this imaginary image
op. As to the place, it is fufficient to remark, that
if the diftance of the object A O be equal to the dis-
tance of the focus of the lens, the image will be at
an infinite diftance from it, and this is what the pre-
fent cafe has in common with the preceding ; but
the nearer the object is brought to the lens, or the
lefs that the diftance AO becomes than that of the
focus of the Iens,the nearer docs the imaginary image
approach to the lens, though, at the fame time, it
remains always at a greater diftance from the lens
than the object itfelf.
To elucidate this by an example, let us fuppofe
that the focal diftance of the lens is 6 inches, and
for the different cliftances of the object, the annexed <(
table indicates the diftance of the imaginary image oj>.
Diftance
SIMPLE CONVEX LENS.
329
Diftance of the Object A O.
Diftance of the imaginary Ima^t
A o.
Infinity
3°
12
6
3
i and a fifth.
The rule for afcertaining the magnitude of this
imaginary image o p is eafy and general, you have
only to draw through the middle of the lens, marked
C, and through the extremity of the object P, the
ftraight line C V p ; and where it meets with the line
o p drawn from o at right angles with the axis of the
lens, you will have found the magnitude of the ima-
ginary image op ; from which it is evident, that this
image is always greater than ths object O P itfelf, as
many times as it is farther from the lens than the
object O P. It is iikewlfe evident, that this image
is not reverfed, as in the preceding cafe, but upright
as the object.
You will eafily comprehend, from what I have
faid, the benefit that may be derived from lenfes of
this fort, by perfons whofe fight is not adapted to
the view of near objects,* but who can fee them to
more advantage at a conficlerable diftance. They
have only to look at objects through a convex lens,
in order to fee them as if they wrere very diftant.
The defect of fight with refpect to near objects oc-
curs ufualiy in aged people, who confequently make
u
3J3 USE AND EFFECT OF
ufe of fpectacles with, convex glaffes, which, expofed
to the fun, produce the effect of a burning-glafs, and
this afcertains the focal diftance of every glafs. Some
perfons have occafion for fpectacles of a very near
focus, others of one more diftant, according to the
ftate of their fight ; but it is fufficient, for my pre-
fent purpofe, to have given a general idea of the ufe
of fuch fpectacles.
12th January. 1762.
LETTER LXXXIH.
Ufe and Effect of a Concave hens.
"\7 OU have feen how convex glaffes aflift the fight
JL of old people, by reprcfenting to them objects
as at a greater diftance than they really are : there are
eyes, on the contrary, which, in order to diftinct vi-
fion, require the objects to be reprefentcd as nearer ;
and concave glaffes procure them this advantage :
which leads me to the explanation of the effect of
concave le'nfes, which is directly the contrary of that
of the convex.
When the object O P, (plate VI. fig. 9.) is very
diftant, and it's rays O M, O M, fail almoft parallel
on the concave lens T V, in this cafe, inftead of be-
coming convergent by the refraction of the lens,
they, on the contrary, become more divergent, pur-
suing the direction N F, N F, which, produced back-
ward, meet at the point 0 ; fo that an eye placed, for .
example, at E, receives thefe refracted rays in the
7 fame
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iri/sf
A CONCAVE LENS. 33 I
fame manner as if they proceeded from the point o>
though they really proceed from the point O ; for
this reafon I have, in the figure, dotted the ftraight
lines N o9 N o.
As the object is fuppofed to be infinitely diftant,
were the lens convex the point o would be what we
call the focus ; but as, in the prefcnt cafe, there is no
real concurrence of rays, we call this point, the ima-
ginary focus of the concave lens ; fome authors like-
wife denominate it the point of difperfion, becaufe the
rays, refracted by the giafs, appear to be difperfed
from this point.
Concave lenfes, then, have no real focus, like the
convex, but only an imaginary focus, the diftance of
which from the lens A o is, however, denominated
the focal diftance of this lens, and ferves, by means
of a rule limilar to that which is laid down for con-
vex lenfes, to determine the place of the image, when
the object is not infinitely diftant. Now this image
is always imaginary, whereas in the cafe of convex
lenfes, it becomes fo only when the objecl is nearer
than the diftance of the focus. Without entering
into the explication of this rule, which refpects cal-
culation merely, it is fufficient to remark :
I. When the objecl: O P is infinitely diftant, the
imaginary image o p is reprefented at the focal dif-
tance of the concave lens, and this too on the fame
fide with the objecl:. Neverthelefs, though this
image be imaginary, the eye placed at E is quite as
much affected by it as if it were real, conformably
to the explanation given on the fubject of convex
lenfes,
352 USE AND EFFECT OF
lenfes, when the object is nearer the lens than it's
focal diftance.
II. On bringing the object O P nearer to the lens,
it's image op will likewife approach nearer, but in
inch a manner, that the image will always be nearer
to the lens than the object is ; whereas, in the cafe
of convex lenfes, the image is more diftant from the
lens than the object. In order to elucidate this more
clearly, let us fuppofe the focal diftance of the con-
cave lens to be 6 inches.
If the Diftarc. of the ObjecT:
The Diftance of the Image
() A is '
o A will be
Infinite
6
3°
5
12
4
6
3
<•>
2
2
i and a half.
III. By the fame rule you may always determine
the magnitude of the imaginary image op. You
draw from the middle of the lens a ttraight line, to
the extremity of the object P, which will pafs through
the extremity p of the image. For, fince the line
P A reprefents a ray coming from the extremity of
the object, this fame ray muft, after the refraction,
pais through the extremity of the image ; but, as
this ray P A paries through the middle of the lens, it
undergoes no refraction ; therefore it muit itfelf
pais through the extremity of the image, at the
point p.
IV. This
A CONCAVE LENS. 333
• IV. This image is not reverfed, but in the fame
pofition with the object ; and it may be laid (down
as a general rule, that whenever the image falls on
the fame fide of the lens that the object is, it is al-
ways reprefented upright, whether the lens be con-
vex or concave ; but when reprefented on the other
fide, of the lens, it is always reverfed ; and this can
take place only in convex lenfes.
V. It is evident, therefore, that the images repre-
fented by concave lenfes are always fmaller than the
objects ; the reafon is obvious, the image is always
nearer than the object ; you have only to look at
the figure to be fatisfied of this truth. Thefe are
the principal properties to be remarked reflecting
the nature of concave lenfes, and the manner in which
objects are reprefented by them.
It is now eafy to comprehend how concave glafies
may be rendered eifentially ferviceable to perfons
whofe fight is fhort. You are acquainted with fome
who can neither read nor write without brineine: the
paper almoft clofe to their nofe. In order, therefore,
to their feeing diftinctly, the object mult be brought
very near to the organ of vifion ; I think I have for-
merly remarked that fuch perfons are denominated
Miopes. Concave lenfes, then, may be made of great
ufe to them, for they reprefent the moft diftant ob-
jects as very near : the image not being farther from
fuch glafies than their focal distance, which, for the
moft part, is only a few inches.
Thefe images, it is true, are much fmaller than the
objects themfelves : but this by no means prevents
334 0F MICROSCOPES IN GENERAL.
diftinclnefs of vifion. A fmall object near, may ap-
pear greater than a very large body at a diftance. In
fact, a two-dreyer piece* appears to the eye greater
than a ftar in the heavens, though that ftar far ex-
ceed the earth in magnitude.
Perfons whofe fight is fhort, or Miopes, have oc-
caiion, then, for glalfes which reprefent objects as
nearer ; fuch are concave lenfes. And thofe whofe
fight is long, or Prefbites, need convex glalfes, which
reprefent to them objects at a greater diftance.
ibth January) 1762.
LETTER LXXXIV.
Of apparent Magnitude, of the Vifual Angle, and of
Micro/ copes in general
I HAVE been remarking, that Miopes are obliged
to make nfe of concave glalfes to affift their vifion
of diftant objects, and that Prefbites employ convex
glailes in order to a more diftin6t vifion of fuch as
are near : each fight has a certain extent, and each
requires a glafs which mall reprefent objects perfectly #
This diftance in the Miopes is very fmall, and in the
Pi-ejbites very great : but there are eyes fo happily
conformed, as to fee nearer and more diftant objects
equally well.
Neverthelefs, of whatever nature any perfon's fight
may be, this diftance is never very fmall : there is no
* A fmall (ilver coin, fomewhat bigger than the pupil of the
eye, in value the forty-eighth part of a crown.
Miope
OF MICPvOSCOPES IN GENERAL. ^^
Miope capable of feeing diftinctly at the diftance of
lefs than an inch ; you muft have obfcrved, that
when the object is brought too clofe to the eye, it
has a very confufed appearance ; this depends on the
ftructure of the organ, which is fuch. in the human
fpecics, as not to admit of their feeing objects very
near. To infects, on the contrary, very diftant ob-
jects are invifible, while they eafily fee fuch as arc
nearer. I do not believe that a fly is capable of fee-
ing the ftars, becaufe it can fee extremely well at the
diftance of the tenth part of an inch, a diftance at
which the human eye can diftinguifh abfolutely no-
thing. This leads me to an explanation of the mi-
crofcope, which reprefents to us the fmalieft object
as if it were very great.
In order to convey a juft idea of it, I muft entreat
you carefully to diftinguifh between the apparent
and the real magnitude of every object. Real mag-
nitude conftitutes the object of geometry, and is in-
variable as long as the body remains in the fame
ftate. But apparent magnitude admits of infinite
variety, though the body may remain always the
fame. The ftars, accordingly, appear to us extremely
fmall, though their real magnitude is prodigious, be-
caufe we are at an immenfe diftance from them.
Were it poflible to approach them, they would ap-
pear greater, from which you will conclude, that the
apparent magnitude depen'ds on the angle formed
in our eyes, by the rays which proceed from the ex-
tremities of the object.
Let PO O (-plate VII, fg. i.j be the 6Bje& of vi-
fion,
336 OF MICROSCOPES IN GENERAL.
lion, which, if the eye were placed at A, would ap"
pear under the angle PAQ, called the vifual angle,
and which indicates to us the apparent magnitude of
the object ; it is evident, on infpecling the figure,
that the farther the eye withdraws from the object,
the fmaller this angle becomes, and that it is poflible
for the greateft bodies to appear to us under a very
fmall vifual angle, provided our diflance from them
be very great, as is the cafe with the flars. But when
the eye approaches nearer to the objecl, and looks at
it from B, it will appear under the vifual angle P B Q,
which is evidently greater than PAQ. Let the eye
advance flill forward to C, and the vifual angle
P C O is ftill greater. Farther, the eye being placed
at D, the vifual angle will be P D Q ; and on advan-
cing forward to E, the vifual angle will be P E Q,
always greater and greater. The nearer, therefore,
the eye approaches to the objecl, the more the vi-
fual angle increafes, and confequently likewife the
apparent magnitude. However fmall the objecl may
be, it is poflible, therefore, to increafe it's apparent
magnitude at pleafure, you have only to bring it fo
near the eye as is neceffary to form fuch a vifual
angle. A fly near enough to the eye may, of con-
fequence, appear under an angle as great as an ele-
phant at the diflance of ten feet. In a comparifon
of this fort, we muft take into the account the dif-
tance at which we fuppofe the elephant to be viewed :
unlefs this is done, we affirm abfolutely nothing ; for
an elephant appears great only when we are not very
far from it ; at the diflance of a mile, it would be
impoffible,
OF MICROSCOPES IN GENERAL. . 337
impoflible, perhaps, to diftinguifti an elephant from a
pig ; and, tranfported to the moon, he would be-
come abfolutely invifible ; and I might affirm with
truth, that a fly appeared to me greater than an ele-
phant, if the latter was removed to a very confider-
able diftance. Accordingly, if we would exprefs
ourfelves with precifion, we muft not fpeak of the
apparent magnitude of a body, without taking dif-
tance likewife into the account, as the fame body
may appear very great or very fmall, according as it's
diftance is greater or lefs. It is very eafy, then, to
fee the fmalleft bodies under very great vifual angles ;
they need only to be placed very clofe to the eye.
This expedient may be well enough adapted to a
fly, but the human eye could fee nothing at too fmall
a diftance, however ftiort it's fight may be ; befides,
perfons of the beft light would wifti to fee likewife
the fmalleft objects extremely magnified. The thing
required, then, is to find the means of enabling us
to view an object diftinctly, notwithftanding it's
great proximity to the eye. Convex lenfes render
us this fervice, by removing the image of objects
which are too near.
Let a very fmall convex lens M N be employed,
(plate VII: Jig. 2.) the foCal diftance of which fhall be
half an inch ; if you place before it a fmall object
O P, at a diftance fomewhat lefs than half an inch?
the lens will reprefent the image of it 0 p, as far off
as could be wilhed. On placing the eye, then, be-
hind the lens, the object will be feen as if it were at
», and at a fufficient diftance, as if it's magnitude
Vol. II. Z were
3$% " OBJECTS VIEWED THROUGH
were op: as the eye is fuppofed very near the lens,
the vifual angle will be p t o, that is the fame as
P t Oy under which the naked eye would fee the ob-
ject O P in that proximity ; but the vifion is become
diftinct by means of the lens : fuch is the principle on
which microfcopes are conftructed.
\tyh January r 1762.
LETTER LXXXV.
Eflimat'iGn of the Magnitude of Objecls viewed through
the Micro/cope,
WHEN feveral perfons view the fame object
through a microfcope, the foot of a fly, for
example, they all agree that they fee it greatly mag-
nified, but their judgment refpe&ing the real mag-
nitude will vary : one will fay, it appears to him as
large as that of a horfe ; another, as that of a goat ,
a third, as that of a cat. > No one, then, advances any
thing pofitive on the fubject, unlefs he adds, at what
diftance he views the feet of the horfe, the goat, or
the cat. They all mean, therefore, without expreffing
it, a certain diftance which is undoubtedly different ;
confequently there is no reafon to be furprized at the
variety of the judgments which they pronounce, as
the foot of a horfe, viewed at a diftance, may very
well appear no bigger than that of a cat, viewed near
to the eye. Accordingly, when the queftion is to be
decided, How much does the microfcope magnify an
object ? we muft accuftom ourfelves to a more accu-
rate
THE MICROSCOPE. 339
rate mode of expreflion, and particularly to fpecify
the diftance, in the comparifbn which we mean to
inftitute.
It is improper, therefore, to compare the appear-
ances prefented to us by the microfcope, with objects
of another nature, which we are accuftomed to view
fometimes near, and fometimes at a diftance. The
m oft certain method of regulating this eftimation
feems to be that which is actually employed by authors
who treat of the microfcope. They compare a fmall
object viewed through the microfcope with the ap-
pearance which it would prefent to the naked eye,
1 on being removed to a certain diftance ; and they
have determined, that, in order to contemplate fuch
fmall objecl: to advantage by the naked eye, it ought
to be placed at the diftance of eight inches, which is
the ftandard for good eyes, for a fhort-fighted perfon
would bring it clofer to the eye, and one far-fighted
would remove it. But this difference does not affect
the reafoning, provided the regulating diftance be
fettled ; and no reafon can be affigned for fixing on
any other diftance than that of eight inches, the dif-
tance received by all authors who have treated of the
fubjeft. Thus, when it is faid that a microfcope mag-
nifies the objecl: a hundred times, you are to under-
ftand that, with the ai&ftance of fuch microfcope, ob-
jects appear a hundred times greater than if viewed
at the diftance of eight inches, and thus you will
form a juft idea of the effect of a microfcope.
In general, a microfcope magnifies as many times
as an objecl: appears larger than if it were viewed
Z 2 without
g4<? OBJECTS VIEWED THROUGH
without the aid of the glafs, at the diftance of eight
inches. You will readily admit that the effect is fur-
prizing, if an object is made to appear even a hundred
times greater than it would to the naked eye, at the
diftance of eight inches : but it has been carried much
farther, and microfcopes have been conftruc~ted,which
magnify five hundred times, a thing almoft incredible.
In fuch a cafe it might be with truth affirmed, that
the leg of a fly appears greater than that of an ele-
phant. Nay I have full conviction, that it is poffible
to conftrud microfcopes capable of magnifying one
thoufand, or even two thoufand times, which would
undoubtedly lead to the difcovery of many things
hitherto unknown.
But when it is affirmed, that an object appears,
through the microfcope, a hundred times greater
than when viewed at the diftance of eight inches, it
is to be underftood that the object is magnified as
much in length, as in breadth and depth, fo that each
of thefe dimenfions appears a hundred times greater.
You have only, then, to conceive, at the diftance of
eight inches, another object fimilar to the firft, but
whofe length is a hundred times greater, as well at
it's breadth and depth, and fuch will be the image
viewed through the microfcope. Now, if the length.,
the breadth and depth of an object, be a hundred
times greater than thofe of another, you will eafily
perceive that the whole extent will be much more
than a hundred times greater. In order to put this
in the cleareft light, let us conceive two parallelograms
ABCD, and ..EFGH, (fate VII. fig. y) of the
fame
THE MICROSCOPE. 34I
fame breadth, but that the length of the firft A B,
fhall be five times greater than the length of the other
EF; it is evident that the area, or fpace contained
in the firft, is five times greater than that contained
in the other, as in facl: this laft is contained live times
in the firft. To render, then, the parallelogram A D,
five times greater than the parallelogram E H, it
is fufficient that it's length A B be five times greater,
the breadth being the fame ; and if, befides, the
breadth were likewife five times greater, it would be-
come five times greater ftill,. that is five times five
times, or twenty-five times greater. Thus, of two
furfaces, if the one be five times longer and five
times broader than the other, it is, in fact., twenty-
five times greater.
If we take, farther, the height or depth into the
account, the increafe will be ftill greater. Conceive
two apartments, the one of which is five times
longer, five times broader and five times higher than
the other ; it's contents will be five times 25 times,
that is 125 times greater. When, therefore, it is
faid that a microfcope magnifies 1 00 times., as this is
to be underftood not only of length, but of breadth
and depth, or thicknefs, that is of three dimenfions,
the whole extent of the object, will be increafed 100
times 100 times 100 times ; now 100 times 100 make
10,000, which taken again 100 times make 1,000,000;
thus when a microfcope magnifies 100 times, the
whole extent of the object is reprefented 1,000,000
times greater. We fatisfy ourfelves, however, with
faying that the microfcope magnifies 1 00 times ; but
Z3 it
342 PLAN OF SIMPLE MICROSCOPES.
it is to be understood that all the three dimensions,
namely,, length, breadth, and depth are reprefented
i oo times greater. If then a microfcope mould
magnify iooo. times, the whole extent of the object:
would become iooo times iooo times iooo times
greater, which makes 1 000,000,00 d, or a thoufand
millions : a moil aftonifliing effect ! This remark is
neceffary to the formation of a juSt idea of what is
faid refpecKng the power of microfcopes.
2$d 'January, l 762.
LETTER LXXXVI.
fundamental Propofttion for the Conftruclion of Simple
Microfcopes. Plan offome Simple Microfcopes.
"AVING explained in what manner we are en-
abled to jud^e of the power of microfcopes,
it will be eafy to unfold the fundamental principle
for the construction of fimple microfcopes. And
here it may be neceifary to remark, that there are
two kinds of microfcopes ; fome confifling of a fingle
lens, others of two or more, named, accordingly,
Simple or compound microfcopes, and which require
particular elucidations. T fhail confine myfelf, at
prefent, to the Smip'e microfcope, which confifts of a
fingle convex lens, the effect of which is determined
by the following proposition : A fimple microfcope mag-
nifies as many times as ifs focal d /fiance is nearer than
eight inches. The demonstration follows.
Xet M N, (plate VII. fig. 4. J be a convex lens,
whofe focal distance, at which the object O P muSt
be
PLAN OF SIMPLE MICROSCOPES. 343
be placed nearly, in order that the eye may fee it
diftinctly, mail be C O; this object will be perceived
under the angle O C P. But if it be viewed at the
diftance of eight inches, it would appear under an
angle as many times fmaller as the diftance of eight
inches furpaffes the diilance C O : the object will ap-
pear, therefore, as many times greater than if it were
viewed at the diftance of eight inches. Now, in con-
formity to the rule already eftablifhed, a microfcope
magnifies as many times as it prefenjts the objeel:
greater than if we viewed it at the diftance of eight
inches. Confequently a microfcope magnifies as
many times as it's focal diftance is lefs than eight
inches. A lens, therefore, whofe focal diftance is an
inch, will magnify precifely eight times ; and a lens
whofe focal diftance is only half an inch, will magnify
fixteen times. The inch is divided into twelve parts,
called lines ; half an inch,, accordingly, contains fix
lines ; hence it would be eafy to determine how
many times every lens, whofe focal diftance is given
in lines, muft magnify ; according to the following
table :
Focal diftance of the lens in lines.
12. 8. 6. 4. 3. 2. 1. 1 lines
magnifies 8. 12, 16. 24. 32. 48. 96. 192 times
Thus a convex lens, whofe focal diftance is one
line, magnifies ninety-fix times, and if the diftance
be half a line, the microfcope will magnify one hun-
dred and ninety-two, that is near two hundred times.
Were greater effect ftill to be defired, lenfes muft be
conftru&ed of a ftill fmaller focus. Now, it has been
Z 4 . already
344 PLAN OF SIMPLE MICROSCOPES.
already remarked that, in order to conftruct. a lens
of any certain given focus, it is only neceffary to
make the radius of each face equal to that focal dis-
tance, fo that the lens may become equally convex
on both fides. I now proceed, then, to place before
you (plate VII. Jig. 5. J the form of fome of thefelenfes
or microfcopes.
I. The focal diftance of this lens A O is one inch or
twelve lines. This microfcope, therefore, magnifies
eight times.
II. The focal diftance of the lens M N is eight lines.
This microfcope magnifies twelve times.
III. The focal diftance of the lens M N is fix lines.
This microfcope magnifies fixteen times.
IV. The focal diftance of this lens is four lines ;
and fuch a microfcope magnifies twenty-four times.
V. The focal diftance here is three lines. This mi-
crofcope magnifies thirty-two times.
VI. The focal diftance here is two lines. This mi-
crofcope magnifies forty-eight times^.
VII. The focal diftance of this lens is only one line ;
and fuch a microfcope magnifies ninety-fix times.
It is poffible to conftruct microfcopes ftill much
fmaller. They are actually executed, and much more
confiderable effects are produced ; whence it muft be
carefully remarked, that the diftance of the object
from the glafs becomes fmaller and fmaller, as it muft
be nearly equal to the focal diftance of the lens. I
fay nearly , as every eye brings the glafs clofer to it,
fomewhat more or lefs, according to it's formation ;
the fliort-fighted apply it clofer, the far-fighted lefs
£0. You perceive then, that the effect is greater, as
the
SIMPLE MICROSCOPE. 345
the microfcope or lens become fmaller, and the clofer
likewife the object muft be applied ; this is a very-
great inconvenience, for, on the one hand, it i»
troublefome to look through a glafs fo very fmall,
and, on the other, becaufe the object muft be placed
fo near the eye. Attempts have been made to re-
medy this inconvenience, by a proper mounting,
which may facilitate the ufe of it j but the vifion of
the object is conliderably difturbed, as foon as the
diftance of it undergoes the flighted change : and as
in the cafe of a very fmall lens, the object muft almoft
touch it, whenever the furface of the object is in the
Jeaft degree unequal, it is feen but confufedly. For,
while the eminences are viewed at the juft diftance,
the cavities being too far removed, muft be feen very
confufedly. This renders it neceffary to lay afide
fimple microfcopes, when we wifh to magnify very
conliderably, and to have recourfe to the compound
microfcope.
zbtb "January 1 1762.
LETTER LXXXVII.
Bounds , and Defefts of the Simple Microfcope,
YOU have now feen how fimple microfcopes may
be conftructed, which mail magnify as many
times as may be defired ; you have only to meafure
off a ftraight line of eight inches, like that which I
have marked A B,* (plate VII. fig. 6. J which contains
* It being impoffible here to prefent a ftraight line of eight
inches, one of four is employed for the purpofe of demonftration.
precifely
34-6 DEFECTS OF THE
precifely eight inches of the Rhenifh foot, which is
the ftandard all over Germany, This line A B muft
then be fubdivided into as many equal parts as cor-
refpond to the number of times you wifh to mag-
nify the object propofed, and one of thefe parts will
give the focal diftance of the lens that is requifite.
Thus, if you wifh to magnify a hundred times, you
muft take the hundredth part of the line A B, confe-
quently, you muft conftruct a lens whofe focal dif-
tance mall be precifely equal to that part A 1 5 which
will give, at the fame time, the radius of the furfaces
of the lens reprefented in article VII, of the preceding
figure. Hence it is evident, that the greater the
effect we mean to produce, the fmaller muft be the
lens, as well as the focal diftance at which the object
O P muft be placed before the lens, while the eye is
applied behind it : and if the lens were to be made
twice fmaller than what I have now defcribed, in
order to magnify two hundred times, it would be-
come fo minute, as almoft to require a microfcope to
fee the lens itfelf ; befides it would be neceffary to
approach fo clofe, as almoft to touch the lens, which,
as I have already obferved, would be very inconver
nient. The effect of the microfcope, therefore, could
hardly be carried beyond two hundred times ; which
is by no means fufficient for the inveftigation of many
of the minuter productions of nature. The pureft
water contains fmall animalcules, which, though mag-
nified two hundred times, ftill appear no bigger than
fleas; and a microfcope which fhould magnify 20,000
times, would be neceffary to magnify their appear-
ance to the fize of a rat, and we are far from reach-
ing
SIMPLE MICROSCOPE. 347
ing this degree, even with the afliftance of the com-
pound microfcope.
But befides the inconveniences attending the ufe
of fimple microfcopes which have been already
pointed out, all thofe who employ them, with a view
to very great effect, complain of another confiderable
defect 5 it is this, the more that objects are magnified,
the more obfcure they appear j they feem as if viewed
in a very faint light, or by moon-light, fo that you
can hardly diflinguifh any thing clearly. You will
not be furprized at this, when you recollect , that the
light of the full moon is more than two hundred
thoufand times fainter than that of the fun.
It is of much importance, therefore, to explain
whence this diminution of light proceeds. We can
eali'y comprehend, that if the rays which proceed
from a very fmall object muft reprefent it to us, as
if it were much larger, this fmall quantity of light
would not be fufficient. But, however well founded
this reafoning may appear, it wants folidity, and
throws only a falfe light on the queftion. For if the
lens, as it proceeded in magnifying, neceffarily pro-
duced a diminution of clearnefs, this muft likewife
be perceptible in the fmalleft effe&s ; even fuppofing
it were not to fo high a degree j but you may mag-
nify up to fifty times without perceiving the leaft ap-
parent diminution of light, which, however, ought
to be fifty times fainter, if the reafon adduced were
juft. We muft look elfe where, then, for the caufe
of this phenomenon, and even refort to the firft prin-
ciples of vilion.
I muft
34-8 DEFECTS OF THE
I mull entreat you, then, to recollect what I have
already fuggefted refpecting the ufe of the pupil, or
that black aperture which we fee in the eye at the
middle of the iris, It is through this aperture that
the rays of light are admitted into the eye ; accord-
ingly, the larger this aperture is, the more rays are
admitted, We mull here confider two cafes, in which
objects are very luminous and brilliant, and in which
they are illuminated by only a very faint light. In
the firft, the pupil contracts of itfelf, without any act
of the will, and the Creator has bellowed on it this
faculty, in order to preferve the interior of the eye
from the too dazzling effect of light, which would
infallibly injure the nerves. Whenever, therefore,
we are expofed to a very powerful light, we obferve
that the pupil of every eye contracts, to prevent the
admiffion of any more rays into the eye than are ne-
ceiTary to paint in it an image fuiHciently luminous.
But the contrary takes place when we are in the dark ;
the pupil, in that cafe, expands to admit the light in
a greater quantity. This change is eafily perceptible
every time we pafs from a dark to a luminous litua-
tion. With refpect to the fubject before us, I confine
myfelf to this circumitance, that the more rays of
light are admitted into the eye, the more luminous
wih be the image tranfmitted to the retina, and re-
ciprocally, the fmaller the quantity of rays which
enter the eye, the fainter does the image become, and
confequently the more obfcure does it appear. It
may happen, that though the pupil is abundantly ex-
panded, a few rays only mail be admitted into the
eye.
SIMPLE MICROSCOPE. 349
eye. You have only to prick a little hole in a card
with a pin, and look at an object through it; and
then, however flrongly illuminated by the fun, the
object will appear dark in proportion as the aperture
is fmall, nay, it is poilible to look at the fun itfelf,
employing this precaution. ' The reafon is obvious,
a few rays only are admitted into the eye: however
expanded the pupil may be, the pin-hole in the card
determines the quantity of light which enters the
eye, and not the pupil, which ufually performs that
function.
The fame thing takes place in the microfcopes
which magnify very much ; for when the lens is ex-
tremely fmall, a very few rays only are tranfmitted,
as m n (plate VII. fig. %.*) which being fmaller than
the aperture of the pupil, make the object appear
fo much more obfcure ; hence, it is evident, that this
diminution of light takes place only when the lens
M N, or rather it's open part, is fmaller than the
pupil. If it were poflible to produce a great magni-
fying effect by means of a greater lens, this obfcurity
would not take place; and this is the true folution of
the queftion. In order to remedy this inconveni-
ence, in the great effects of the microfcope, care is
taken to illuminate the object as flrongly as poilible,
to give greater force to the few rays which are con-
veyed into the eye. To this effect objects are illu-
minated by the fun itfelf, mirrors likewife are em-
ployed, which reflect on them the light of the fun.
Thefe are, nearly, all the circumftances to be con-
fidered refpecting the fimple microfcope, and by thefe
you
35° ON TELESCOPES,
you will eafily form a judgment of the effect, of all
thofe which you may have occafion to infpect..
$otb January, 1762.
LETTER LXXXVIII.
On Telej 'copes , and their Effecl.
iEFORE I proceed to explain the conftruction of
compound microfcopes, a digrellion refpecling
the telefcope may perhaps be acceptable. Thefe two
inflruments have a very intimate connection : the
one greatly aflifts the elucidation of the other. As
microfcopes ferve to aid us in contemplating nearer
objects, by reprefenting them under a much greater
angle than when viewed at a certain diftance, fay
eight inches ; fo the telefcope is employed to afuft
our obfervation of very diftant objects, by repre-
fenting them under a greater angle than that which
they prefent to the naked eye. Inflruments of this
fort are known by feveral names, according to their
fize and ufe ; but they muft be carefully diflinguifhed
from the glaffes ufed by aged perfons to relieve the
decay of light.
A telefcope magnifies as many times as it repre-t
fents objects under an angle greater than is prefented
to the naked eye. The moon, for example, appears
to the naked eye under an angle of half a degree,
confequently,a telefcope magnifies one hundred times,
when it reprefents the moon under an angle of fifty
degrees, which is one hundred times greater than
1 half
AND THEIR EFFECT. 35 I
half a degree. If it magnified two hundred times, it
would reprefent the moon under an angle of one
hundred degrees : and the moon would, in that cafe,
appear to fill more than half of the vifible heavens,
whofc whole extent is only one hundred and eighty
degrees.
In common language, we fay that the telefcope
brings the abject nearer to us. This is a very equi-
vocal mode of exprefiion, and admits of two different
Significations. The one, that on looking through a
telefcope, we coniider the object as many times nearer
as it is magnified. But I have already remarked,
that it is impoiTiH to know the diitance of objects
but by actual me. urement, and that fuch meafure-
ment can be applied only to objects not greatly re-
mote ; when, therefore, they are fo remote as is here
fuppofed, the eftimation of diftance might greatly
miflead us. The other fignification, which conveys
the idea, that telefcopes reprefent objects as great as
they would appear, if we approached nearer to them,
is more conformable to truth. You know that the
nearer we come to any object, the greater becomes
the angle under which it appears ; this explanation,
accordingly, reverts to that with which I fet out.
When, however, we look at well-known objects, fay
men, at a great diftance, and view them through a
telefcope under a much greater angle, we are led to
imagine fuch men to be a great deal nearer, as, in
that cafe, we would, in effect, fee them under an angle
fo much greater. But in examining objects lefs ap-
proachable, fuch as the fun and moon, no meafure-
rnent
352 ON TELESCOFESj
ment of diftance can take place. This cafe is en*
tirely different from that which I have formerly fub*
mitted to you, that of a concave lens, employed by
near-fighted perfons, which reprefents the images of
objects at a very fmall diftance. The concave lens
which I ufe, for example, reprefents to me the images
of all remote objects, at the diftance of four inches $
it is impofllble for me, however, to imagine that the
fun, moon, and ftars are fo near ; accordingly we do
not conclude that obje&s are where their images are
found reprefented by glafles : we believe this as little
as we do the exiftence of obje&s in our eyes, though
their images are painted there. You will pleafe to
recollect that the eftimation of the real diftance^ and
real magnitude of objects, depends on particular cir-
cumftances.
The principal end of telefcopes, then, is to increafe,
or multiply, the angle under which objects appear to
the naked eye; and the principal divifion of telefcopes
is eftimated by the effect which they procure. Ac*
cordingly we fay fuch a telefcope magnifies five, ano-
ther ten, another twenty, another thirty times, and
fo on. And here I remark that pocket-glaffes rarely
magnify beyond ten times ; but the ufual telefcopes
employed for examining very diftant terreftrial ob-
jects magnify from twenty to thirty times ; and theif
length amounts to fix feet or more. A fimilar effect,
though very confiderable with regard to terreftrial
objects, is a mere nothing with refpect to the hea-
venly bodies, which require an effecl; inconceivably
greater. We have, accordingly, aftronomical tele-
fcopes,
OF pocket glasses; 2>SZ
(copes, which magnify from fifty to two hundred
times ; and it would be difficult to go farther, as ac-
cording to the ufual mode of conftrucling them, the
greater the effect is, the longer they become. A te-
lefcope that fhall magnify one hundred times muft be
at leaft thirty feet long ; and one of a hundred feet
in length could fcarcely magnify two hundred times.
You muft be fenfible, therefore, that the difficulty of
pointing and managing fuch an unwieldy machine,
muft oppofe infurmountable obftacles to pufhing the
experiment farther. The famous Hevelius, the aftro-
nomer at Dantzick, employed telefcopes two hundred
feet long ; but fuch inftruments muft, undoubtedly,
have been very defective, as the fame things are now
difcovered by inftruments much fhorter.
This is a brief general defcription of telefcopes,
and of the different kinds of them, which it is of im-
portance carefully to remark, before we enter into a
detail of their conft ruction, and of the manner in
Which two or more lenfes are united^ in order to
produce all the different effects.
%d February, 1762.
LETTER LXXXIX.
Of Pocket-Glajes.
"TX7E have no certain information refpecting* the
perfon to whom we are indebted for the dif-
covery of the telefcope ; whether he were a Dutch
artift, or an Italian of the name of Porta. Whoever
.V01,. II. A a he
354 °F POCKET GLASSES.
he was, it is almoft one hundred and fifty years fincc
fmail pocket glaffes were firft conftructed, compofed
of two lenfes, of which the one was convex, and
the other concave. To pure chance, perhaps, a dif-
covery of fo much utility is to be afcribed. It was
poflible, without defign, to place two lenfes nearer to,
or farther from each other, till the object appeared
diftircT/.y.
The convex lens PAP (plate VII. Jig. g.J is di-
rected toward the object, and the eye is applied to
the concave lens QBQ: for which reafon the lens
PAP is named the objective, and QBQ the ocular
lens. Thefe tv/o lenfes are difpofed on the fame axis
AB, perpendicular to both, and palling through their
centres; The focal diftance of the convex lens PAP
mult be greater than that of the concave ; and the
lenfes muft be difpofed in fuch a manner, that if AF
be the focal diftance of the objective PAP, the focus
of the ocular QBQ muft fall at the fame point F;
accordingly, the interval between the lenfes A and B,
is the difference between the focal diftances of the
two lenfes, AF being the focal diftance of the ob-
jective, and BF that of the ocular. When the lenfes
are arranged, a perfori with good eyes will clearly
fee diftant objects, which will appear as many times
greater as the line AF is greater than BF. Thus,
fuppoiing the focal diftance of the objective to be fix
inches, and that of the ocular one inch, the object:
will be magnified fix times, or will appear under an
an^ie fix times greater than when viewed with the
naked ;- ■., and, in this cafe, the interval t . •• n the
lenfes
OF POCKET GLASSES. 355
lenfes A and B will be five inches, which is, at the
fame time, the length of the inftrument. There is
no need to inform you that thefe two lenfes are cafed
in a tube of the fame length, though not thus repre-
fented in the figure.
Having fhewn in what manner the two lenfes are
to be joined together in order to produce a good in-
ftrument, two things muft be explained to you : the
one, How thefe lenfes come to reprefent objects dis-
tinctly ; and the other, Why they appear magnified
as many times as the line AF exceeds the line BF.
With refpect to the firft, it muft be remarked, that a
good eye fees objects beft, when they are fo diftant
that the rays which fall on the eye may be confidered
, as parallel to each other.
Let us confider, then, a point V (plate VII. Jig. io.^J
in the object toward which the inftrument is directed,
and on the fuppofition of it's being very diftant, the
rays which fall on the objective PQ, OA, PO, will
be almoft parallel to each other ; accordingly, the ob-
jective QAO, being a convex lens, will collect them
in it's focus F, fo that thefe rays, being convergent,
will not fuit a good eye. But the concave lens at B,
having the power of rendering the rays more diver-
gent, of of diminifhing their convergency, will re-
fract the rays OR, QR, fo that they {hall become
parallel to each other ; that is, inftead of meeting in
the point F, they will affume the direction RS, RS,
parallel to the axis BF. Thus a good eye, according
to which the construction of thefe is always regu-
lated, on receiving thefe parallel rays RS, BF, RS,
A a 2 will
356 OF POCKET GLASSES.
will fee the object diftinctly. The rays RS, RS, be-
come exactly parallel to each other, becaufe the con-
cave lens has it's focus, or rather it's point of difper-
fion, at F.
You have only to recoiled that, when parallel
rays fall on a concave lens, they become divergent
by refraction, fo that being produced backward, they
meet in the focus. This being laid down, we have
only to reverfe the cafe, and to confider the rays SR,
S R, as falling on the concave lens ; in this cafe it is
certain they would affume the directions RQ, RQ,
which, produced backward, would meet in the point
F, which is the common focus of the convex and
concave lenfes. Now it is a general law, that in
whatever manner rays are refracted in their paffage
from one place to another, they muft always undergo
the fame refractions in returning from the laft to the
ftrft. If, therefore, the refracted rays RQ, RQ, cor-
tefpond to the incident rays S R, S R ; then, recipro-
cally, the rays OR, QR, being the incident, the re-
fracted rays will be RS and RS.
The matter will, perhaps, appear in a clearer light
ftill, when I fay, that concave lenfes have the power
of rendering parallel thofe rays which, without the
refraction, would proceed to their focus. You will
pleafe carefully to attend to the following laws of
refraction, which apply to both convex and concave
lenfes.
I. By a convex lens {plate VII. Jig, 11.) parallel
rays are rendered convergent.
Convergent
TlcUel/II
■fk
Fy.y.
J5
>c ,,.
G
"^^ """""---
F$.fi
Fuc
*?■
#•
^.^
fuzstcUtJA
OF POCKET GLASSES, 357
Convergent rays become ftill more fo, {plate VIII,
fig. 1.) and divergent lefs divergent.
IL By a concave lens parallel rays are rendered
divergent. {Plate VIII. fig. 2.)
Divergent rays become Hill more divergent,^. 3.
and convergent rays lefs convergent.
All this is founded on the nature of refraction, and
the figure of the lenfes, the difcuffion of which would
require a very long derail ; but the two rules which
I have now laid down, contain all that is elTential.
It is abundantly evident, then, that when the convex
and the concave lenfes are fo combined, that they
acquire a common focus at F, they will diftinclly rev-
prefent diftant objects, becaufe the parallelifm of the
rays is reftored by the concave lens, after the con-
vex lens had rendered them convergent. In other
words, the rays of very diftant objects, being nearly
parallel to each other, become convergent by a con-
vex lens, and afterwards, the concave lens deftroys
this convergency, and again renders the rays parallel
to each other.
6tb February, lj6z.
LETTER XC.
On the magnifying Power of Pocket Glafles
r I "'HE principal article reflecting telefcopical in-
-*- ftruments, remains ftill to be explained, namely,
their effect in magnifying objects. I hope to place
^his ill fo clear a light, as to remove every difficulty
JTa 3 in
358 MAGNIFYING POWER OF
in which the fubject may be involved ; and for this
purpofe I mall comprize what I have to fay, in the
following propolitions.
I. Let E e: {plate VIII. fig. 4.) be the object, fku-
ated on the axis of the inftrument which paffes per-
pendicularly through both lenfes in their centres.
This object E e muft be confidered as at an infinite
diftance.
II. If then the eye, placed at A, looks at this ob-
ject, it will appear under the angle EA<?, called it's
vifual angle. It will, accordingly, be neceifary to
prove, that on looking at the fame object through
the glafs, it will appear under a greater angle, and
exactly as many times greater as the focal diftance
of the objective lens PAP exceeds that of the ocu-
lar OBQ.
III. As the effect of all lenfes confifts in reprefent-
ing the objects in another place, and with a certain
magnitude, we have only to examine the images
which fhall be fucceffively reprefented by the two
lenfes, the laft of which is the immediate object of
the fight of the perfo'n who looks through the in-
ftrument.
IV. Now, the object E e being infinitely diftant
from the convex lens PAP, it's image will be repre-
fented behind the lens at ~Ff, fo that AF mail be
equal to the focal diftance of the lens ; and the mag-
nitude of this image F/- is determined by the ftraight
line fA e drawn from the extremity of the object e
through the centre of the lens A, by which we fee
that this image is inverted, and as many times fmaller
than
, pock'et glasses. 359
than the object, as the diftance AF is fmaller than
the diftance AE.
V. Again, this image Yf holds the place of the
object, relatively to the ocular lens OB Q : as the
rays which fall on this lens are precifely thofe which
would almoft form the image Yf, but are intercepted
in their progrefs by the concave lens O B O ; fo that
this image is only imaginary j the effect, however,
is the fame as if it were real.
VI. This image Ff, which we are now confider-
ing as an object, being at the focal diftance of the
lens QBQ, will be tranfported, almoft to infinity, by
the refraction of this lens. The preceding figure
marks this new image at Gg, whofe diftance AG
•muft be conceived as infinite, and the rays, refracted
a fecond time by the lens QBO, will purfue the
fame direction as if they actually proceeded from the
image Gg.
VII. This fecond image Gg being, then, the ob-
ject of the perfon who looks through the inftrument,
it's magnitude falls to be confidefed. To this effect,
as it is produced by the firft image Ff from the re-
fraction of the lens QBO, following the general
rule, we have only to draw' through the centre of
the lens B a ftraight line, which fhall pafs through
the pointy of the firft image, and that line will mark,
at g, the extremity of the fecond image.
VIII. Let the fpectator now apply his eye to B ;
and as the rays which it receives purfue the fame di-
rection as if they actually proceeded from the image
Gg, it will appear to him under the angle GBg,
A a 4 which
360 MAGNIFYING flDWER OF
which is greater than the angle EAf, under which
the object E e appears to the naked eye.
IX. In order the better to c©mpare thefe two,
angles, it is evident, firft, that the angle E A e is equal
to the angle FA/, being vertical angles ; for the
fame reafon the angle GBg is equal to the angle
FB/, being vertical and oppolite at the point B. It
remains to be proved, therefore, that the angle
FB/ exceeds the angle FA/ as many times as the
Jine AF exceeds the line B/; the former of which,
AF, is the focal diftance of the objective, and the
other, BF, the focal diftance of the ocular.
X. In order to demonftrate this, we muft have re-
courfe to certain geometrical proportions refpecting
the nature of fe&ors. You will recoiled!: that the
fector is part of a circle contained between two radii
CM and CN, and an arch or portion of the circum-
ference MN. In a feclior, then, there are three things
to be confidered; 1. The radius of the circle, CM
or CN: 2. The quantity of the arch MN: 3. The
angle MCN.
XI. Let us now confider two fectors, MCN and
men (plate VIII. Jig. 5. J whofe radii CM and cm
are equal to each other : now it is demonftrated in
the elements of geometry, that the angles C and c
have the fame proportion to each other, that the
arches MN and m n have ; in other words, the angle
C is as many times greater than the angle e, as the
arch MN is greater than the arch nm : but, inftead
of this aukward mode of expreffion, we fay, that
POCKET GLASSES. 361
the angles G and c are proportional to the arches
MN and m n, the radii being equal.
XII. Let us likewife confider two fectors, MCN
and men (jig. 6. J whofe angles C and e are equal
to each other, but the radii unequal : and it is de-
monftrated in geometry, that the arch MN is as
many times greater than the arch m n9 as the radius
CM is greater than the radius em: or, in geome-
trical language, the arches are in proportion to the
radii, the angles being equal. The reafon is obvious ;
for every arch contains as many degrees as it's angle ;.
and the degrees of a great circle exceed thofe of a
fmall one as many times as the greater radius ex-
ceeds the fmaller.
XIII. Finally, let us confider likewife the cafe when,
as in the two fe&ors MCN and m c n (Jig. y.J the
arches MN and m n are equal, but the radii CM and
cm unequal.
In this cafe, the angle C, which correfponds to the
greater radius CM, is the fmaller, and the angle c,
which correfponds to the fmaller radius c m, is the
greater, and this in the fame proportion as the radii.
That is, the angle e is as many times greater than
the angle C, as the radius CM is greater than the
radius cm: or, to fpeak geometrically, the angles
are reciprocally proportional to the radii, the arches
being equal.
XIV. This laft propofition carries me forward to
my conclufion, after I have fubjoined this remark,
that when the angles are very fmall, as in the cafe
of pocket-glalTes, there is no fenfible difference in the
chords
362 DEFECTS OF POCKET GLASSES.
C-hords of the arches MN and m », that is of the
.ftraight lines MN, and m n.
XV. Having made this remark, we return to fig. 4.
The triangles FA/ and FB/ may be considered as,
fectors, in which the arch F/ is the fame in both.
Confequently the angle FB/ exceeds the angle FA/
as often as the diftance AF exceeds the diftance BF.
That is, the object E e will appear through the in-
ftrument, under an angle as many times greater as
the focal diftance of the objective AF exceeds the
focal diftance of the ocular BF: which was the thing
to be demonftrated.
qtb February, lj6z.
BETTER XCI.
Defecls of Pocket Glajfes. Of the apparent Field.
"OU muft beTenlible that no great advantage is
to be expected from fuch fmall inftruments ;
and it has already been remarked that they do not
magnify objects above ten times. Were the effect
to vbe carried farther, not only would the length be-
come too great to admit of their being carried about
in the pocket, but they would become ftfbject to
other and more eifential defects. This has induced
artifts entirely to lay afide glaffes of this fort, when
fuperior effect is required.
The principal of thefe defects is the fmallnefs of
the apparent field ; and this leads me forward to ex-
plain an important article relating to telefcopes of
' everv
DEFECTS OF POCKET GLASSES 363
every description. When a telefcope is directed to-
ward the heavens, or to very diftant objects on the
earth, the fpace difcovered appears in the figure of
a circle, and we fee thofe objects only which are in-
cluded in that fpace 5 fo that if you wifhed to exa-
mine other objects, the poiition of the inftrument
muft be altered. This circular fpace, prefented to
the eye of the fpectator, is denominated the apparent
field, or, in one word, the field of the inftrument :
and it is abundantly obvious, that it muft be a great
advantage to have a very large field, and that, on
the contrary, a fmall field is a very great inconve-
nience, in inftruments of this fort. Let us fuppofe
two telefcopes directed toward the moon, by the
qne of which we can difcover only the half of that
luminary, whereas by the other we fee her whole
body, together with the neighbouring ftars ; the field
of this laft is, therefore, much greater than that of
the other. That which prefents the greater held re-
lieves us not only from the trouble of frequently
changing the pofition, but procures another very
great advantage ; that of enabling us to compare, by
viewing them at the fame time, feveral parts of the
object, one with another.
It is, therefore, one of the greateft perfections of
a telefcope to prefent a very ample field ; and it is,
accordingly, a matter of much importance to mea-
fure the field of every inftrument. In this view, we
are regulated by the heavens, and we determine the
circular fpace feen through a telefcope, by meafuring
it's diameter in degrees and minutes. Thus, the ap-
parent
364 DEFECTS OF POCKET GLASSES.
parent diameter of the full moon, being about half
a degree, if a telefcope takes in the moon only, we
fay that the diameter of it's field is half a degree ;
and if you could fee at once only the half of the
moon, the diameter of the field would be the quarter
of a degree.
The measurement of angles, then, furnifhes the
means of meamring the apparent field ; befides, the
thing is fuficiently clear of itfelf. Suppofing we
could fee through the inftrument AB (plate VIIU
Jig, S.J only the fpace POP, and the objecls which
it contains : this fpace being a circle, it's diameter
will be the line POP, whofe middle point O is in the
axis of the inftrument. Drawing, therefore, from
the extremities PP the ftraight lines PC, PC, the
angle PCP will exprefs the diameter of the apparent
field, and the half of this angle QCP is denominated
the femi-diameter of the apparent field of fuch an
inftrument. You will perfectly comprehend the
meaning, then, when it is faid that the diameter of
the apparent field of fuch an inftrument is one de-
degree, that of another two degrees, and fo on 5 as
alfo when it is marked by minutes, as 30 minutes
which make half a degree, or 15 minutes which
mike the fourth part of a degree.
But in order to form a right judgment of the
value of a telefcope, with refpect. to the apparent field,
we muft likewife attend to the magnifying power of
the inftrument. It may be remarked, in general,
that the more a telefcope magnifies, the fmaller, of
neceility, muft be the apparent field j thefe are the
bounds
DEFECTS OF POCKET GLASSES. 365
bounds which nature herfelf has prefcribed. Let us
iiippofe an inftrument which mould magnify ioo
times ; it is evident that the diameter of the field
could not poflibly be fo much as two degrees : for.
as this fpace would appear ioo times greater, it
would referable a fpace of two hundred degrees;
greater, of confequence, than the whole viiible hea-
vens, which, from the one extremity to the other,
contain only 180 degrees, and of which we can fee
but the half at moft at once, that is a circular fpace
of 90 degrees in diameter. From this you fee, that
a telefcope which magnifies ioo times could not con-
tain a field of fo ' much as one degree ; for this de-
cree multiplied ioo times would give more than 90
degrees; and that, accordingly, a telefcope which
magnified 100 times would be excellent, if the dia-
meter of it's field were fomewhat lefs than one de-
gree : and the very nature of the inurnment admits
not of a greater effect
But another telefcope, which lhould magnify only
10 times, would be extremely defective, if it difco-
vered a field of only one degree in diameter ; as this
field magnified 1 o times would give a fpace «£ no
more than ten degrees in the heavens, which would
be a fmall matter, by fetting too narrow bounds to
our view. We fhould have good reafon, then, to
reject fuch an inftrument altogether. Thus it would
be very eafy, with refpect to the apparent field, to
form a judgment of the excellence or defecKvenefs
of inftruments of this fort, when the effeel is taken
into confederation. For when it magnifies only 10
times,
$66 DEFECTS OF POCKET GLASSES.
times, it may fairly be conjectured, that it difcovers
a field of 9 degrees ; as 9 degrees taken 1 o times give
90 degrees, a fpace which our light is capable of em>
bracing : and if the diameter of it's field were only
5 degrees, or lefs, this would be an inftrument very
defective indeed. Now I fhall be able to demon-
strate, that if a telefcope were to be conftructed fuch
as I have been defcribing, which fhould magnify
more than 10 times, it would be liable to this de-
fect : the apparent field multiplied by the magnify-
ing power would be very confiderably under 90 de-
grees, and would not even fhew the half. But when
a fmail effect is aimed at, this defect is not fo fen-
fible; for if fuch an inftrument magnifies only
5 times, the diameter of it's field is about 4 degrees,
which, magnified 5 times, contains a fpace of 20 de-
grees, with which we have reafon to be fatisfied :
but 'if we wifhed to magnify 25 times, the diameter
of the field would be only half a degree, which
taken 25 times, would give little more than 12 de-
grees, which is too little. When therefore we would
magnify very much, a different arrangement of
lenfes muft be employed, which I fhall afterward
explain.
1 yb February, 1762.
LETTER
POCKET GLASSES. 367
LETTER XCil.
Determination of the apparent Field for Pocket Glafes.
rTPO ascertain the apparent field being of very
^ great importance in the conftruction of tele-
fcopes, I proceed to the application of it to the fmall
glalfes which I have been defcribing.
The lens PAP, (plate VIII. fig. 4.) is the objective,
Q B O the ocular, and the ftraight line E F the axis
of the inftrument, in which is feen, at a very great
diftance, through the inftrument, the obje£t E e,
under the angle EA^ which reprefents the femi-
diameter of the apparent field, for it extends as far
on the other fide downward. The point E, then,
is the centre of the fpace feen through the inftrument,
the radius of which, E A, as it paries perpendicularly
through both lenfes, undergoes no refraction ; and
in order that this ray may have admiflion into the
eye, the eye rnuft be fixed fomewhere on the axis
of the inftrument B F, behind the ocular lens, fo that
the centre of the pupil fhall be in the line B F ; and
this is a general rule for every fpecies of telefcope.
Let us now confider the vifible extremity of the ob-
ject <?, whofe rays exactly fill the whole opening of
the objective lens PAP; but it will be fufflcient to
attend only to the ray E A, which paries through
the centre of the objective A, as the others furround;,
and little more than ftrengthen this ray ; fo that if
it is admitted into the eye, the others, or at lea ft a
3 coniiderable
368 DETERMINATION OF THE APPARENT
coniiderable part of them, find admiffion likewife ;
and if this ray is not admitted into the eye, though
perhaps fome of the others may enter, they are too
feeble to excite an impreffion fufficiehtly powerful.
Hence, this may be laid down as a rule, that the ex»
tremity e of the object is feen, only fo far as the ray
e A, after having paffed through the two lenfes, is
admitted into the eye.
We muff, therefore, carefully examine the direc-
tion of this ray e A. Now, as it paffes through the
centre of the objective A, it undergoes no refraction 5
conformably to the rule laid down from the begin-
ning, That rays pailing through the centre of any
lens whatever are not diverted from their direction,
that is, undergo no refraction. This ray, e A, there-
fore, after having paffed through the objective, would
continue in the fame direction, to meet the other
rays iffuing from the fame point e, to the pointy" of
the image reprefented by the objective at F f9 the
point /being the image of the point e of the object ;
but the ray meeting, at m\ the concave lens, but not:
in it's centre, will be diverted from that direction ;
and inftead of terminating in/, will affume the di-
rection m n, more divergent from B F, it being the
natural effect of concave lehfes to render rays al-
ways more divergent. In order to afcertain this
new direction m n, you will pleafe to recollect that
the objective lens reprefents the object E e in ari
inverted pofition at ¥f, fo that A F is equal to the
focal diitance of this lens, which tranfports the ob-
ject E e to ¥ f. Then this image ¥ f occupies the
place
FIELD FOR POCKET GLASSES. 369
place of the object, with refpect to the ocular lens
Q B Q, which, in it's turn, tranfports that image to
G g, whofe diflance B G muft be as great as that of
the object itfelf ; and for this effect, it is neceffary to
place the ocular lens in fuch a manner that the inter-
val B F fhall be equal to it's focal diflance.
As to the magnitude of thefe images, the firil ¥f
is determined by the ftraight line e Af drawn from
e through the centre A of the firft lens ; and the
other G g by the ftraight line f B g drawn from the
point f through the centre B of the fecond lens.
This being laid down, the ray A m directed toward
the point/ is refracted, and proceeds in the direc-
tion m n \ and this line m n being produced backward
will pafs through the point g, for m n has the fame
effect in the eye, as if it actually proceeded from the
point g. Now, as this line m n retires farther and
farther from the axis B F, where the centre of the
pupil is, it cannot enter into the eye, unlefs the
opening of the pupil extends fo far ; and if the open-
ing of the pupil were reduced to nothing, the ray
m n would be excluded from the eye, and the point
e of the object could not be viiible, nor even any
other point of the object out of the axis A F. There
would, therefore, be no apparent field, and nothing
would be feen, through fuch an inftrumcnt, except
the fmgle point E of the object, which is in it's axis.
It is evident, then, that a telefcope of this fort difco-
vers no field, but as far as the pupil expands, fo that
in proportion as the expaniion of the pupil is greater
or lefs, fo likewife the apparent field is great or fmall.
Yol. II. B b In
37© POCKET GLASSES.
In this cafe, the point e will therefore be ftill vifible
to the eye, if the fmall interval B m does not exceed
half the diameter of the eye, that the ray m n may
find admiftion into it ; but in this cafe, likewife, the
eye muft be brought as clofe as poflible to the ocular
lens : for as the ray m n removes from the axis F B,
it would efcape the pupil at a greater diftance.
Now it is eafy to determine the apparent field
which fuch an inftrument would difcover on the
ocular lens : you have only to take the interval B m
equal to the femi-diameter of the pupil, and to draw
through that point m, and the centre of the objective
lens A, the ftraight line m A ?, then this line will
mark on the object the extremity e, which will be
ilill vifible through the inftrument, and the angle
E A e will give the femi-diameter of the apparent
field. Hence you will eafily judge, that whenever
the diftance of the lenfes A B exceeds fome inches,
the angle BAm muft become extremely fmall, as the
line or the diftance B m is but about the twentieth
part of an inch. Now if it were intended to magnify
very much, the diftance of the lenfes muft become
confiderable, and the confequence would be, that the
apparent field muft become extremely fmall. The
ftructure of the human eye, then, fets bounds to
telefcopes of this defcription, and obliges us to have
recourfe to others of a different conftruction, when-
ever we want to produce very confiderable effect.
ibth February t 1762.
LETTER
ASTRONOMICAL TELESCOPES. 37 1
LETTER XCIH.
Agronomical Tele/copes, and their magnifying Powers.
PROCEED to the fecond fpecies of telefcopes9
called aftronomical, and remark that they confifl
of only two lenfes, like thofe of the firft fpecies ; with
this difference, that in the conftru&ion of aftrono-
mical telefcopes, inftead of a concave ocular lens, we
employ a convex. ,
The objeaive PAP (plate VIII. fig. 9.) is, as in the
other fpecies, convex, whofe focus being at F, we fit,
on the fame axis, a fmaller convex lens O Q, in fuch
a manner that it's focus mail likewife fall on the
fame point F. Then placing the eye at O, fo that
the diftance B O mail be nearly equal to the focal
diftance of the ocular Q Q, you will fee objects dif-?
tinctly, and magnified as many times as the focal dik
tance of the objective A F fhall exceed that of the
ocular B F : but it is to be remarked that every ob-
ject will appear in an inverted pofition, fo that if the
inftrument were to be pointed toward a houfe, the
roof would appear under moft, and the grounds-floor
uppermoft. As this circumftance would be aukward
in viewing terreftrial objects, which we never fee in
an inverted fituation, the ufe of this fpecies of tele-
fcopes is confined to the heavenly bodies, it being a
matter of indifference in what direction they appear s
it is fuflicient to the aftronomer to know that what
he fees uppermoft is really undermoft, and recipro-
B b 2 cally.
372 , ASTRONOMICAL TELESCOPES, AND
cally. Nothing, however, forbids the application of
fuch telefcopes to terreftrial objects ; the eye foon.
becomes acciiftomed to the inverted pofition, pro-
vided the object is feen diftinctly and yery much,
magnified.
Having given this defcription, three thing? fall
to be demonftrated : firft, that by this arrangement
of the lenfes objects muft appear diftinctly; fecondly,
that they muft appear magnified as many times as
the focal diftance of the objective lens exceeds that
of the ocular, and in an inverted pofition ; and
thirdly, that the eye muft not be applied clofe to the
ocular lens, as in the firft fpecies, but muft be re-
moved to nearly the focal diftance of the ocular.
i. As to the firft, it is demonftrated m the fame
manner as in the preceding cafe : the rays e P, e P,
which are parallel before they enter into the pbjec-
tive lens, meet by refraction in the focus of this lens
at F ; the ocular lens muft, of courfe, reftore the pa-
rallelifm of thefe rays, and diftinct vifion requires
that the rays, proceeding from every point, mould
be nearly parallel to each other when they enter the
eye. Now, the ocular lens, having it's focus at F, is
placed in fuch a manner as to render the rays F M,
F M, by the refraction, parallel, and confequently the
eye will receive the rays N o9 N o, parallel to each
other.
2, With refpect to the fecond article, let us con-
iider the object at E e, (plate VIII. fig. 10.) but fo as
that the diftance E A fhall be almoft infinite. The
image of this object, reprefented by the objective
lens,
THEIR MAGNIFYING POWERS. 373
lens, Will therefore be F f, fituated at the focal dif-
tance of that lens A F, and determined by the ftraighf.
line e A f, drawn through the centre of the lens.
This image Ff, which is inverted, occupies the plate
of the Object, with refpect to the ocular lens, and be-
ing in it's focus, the fecond image will be again re~
moved to an infinite diftance by the refraction of
this lens, and will fall, for example, at G gy the dif-
tance A G being cOnfidered as infinite, like that of
A E. Now, in order to determine the magnitude
of this image, ydu have only to draw through the
centre B of the lens, and the extremity f of the firft
image, the fttaight line B/g. Now this fecond image
G g being the immediate object of vifion to the per-
fon who looks through the telefcope, it is evident at
once that this reprefentation is inverted ; and, as it is
infinitely diftant, will appear under an angle GB^.
But the object, itfelf E e will appear to the naked eye
Under the angle E A e : now you are fenfible, with-
out being reminded, that it is indifferent to take the
points A and B, in order to haVe the vifual angles
E A e and GB^, on account of the infinite diftance
of the object". You now fee here, as in the preceding
cafe, that the triangles F Ay and F By may be cOn-
fidered as circular fectors, the line Fy meafuring the
arch of both, and the angles themfelves being fo very
fmall, no fenfible miftake can be committed in taking:
the chord for the arch. As, then, the radii of thefe
two fectors are the lines A E and B F, the arches
being equal to each other, it follows, as was formerly
demonftrated, that the angles F A/ (or, which is the
B b 1 fame
374 OF THE APPARENT FIELD, AND
fame thing, E A e ) and F Bf (or, which is the fame
thing, GB gj have the fame proportion to each
other that the radii B F and A F have. Therefore,
the angle GB^, under which the object is feen
through the telefcope, as many times exceeds the
angle E A e , under which the object is feen by the
naked eye, as the line A F exceeds the line BF;
which was the fecond point to be demonftrated. I
am under the neceffity of deferring the demonftra-
tion of my third proportion till next poft.
2.0th February , 1762.
LETTER XCIV.
Of the apparent Field, and the Place of the Eye.
TN fulfilling my engagement refpe£ting the third
-*- particular propofed, namely to determine the
place of the eye behind the telefcope, I remark that
this article is moft intimately connected with the ap-
parent field, and that it is precifely the field which
obliges us to keep the eye fixed at the proper dis-
tance 5 for if it were to be brought clofer, or re-
moved farther off, we should no longer difcover fo
large a field.
The extent of the field being an article of fuch im-
portance, indeed fo effential, in all telefcopes, it muft
be of equal importance to determine exactly the place
of the eye from which the largeft field is difcoverable.
If the eye were to be applied clofe to the ocular lens,
we fhould have nearly the fame field as we have
3 with
>iJT
-Pla-teYITr
THE PLACE OF THE EYE. 2>J$
•with the pocket-glafs, which becomes infufFerab|y
fmall, whenever the magnifying power is consider-
able. It is, therefore, a vaft advantage to agrono-
mical telefcopes, that by withdrawing the eye from
the ocular lens, the apparent field increafes to a Cer-
tain extent i and it is precifely this which renders
fuch telefcopes mfceptible of prodigious magnifying
powers, whereas thofe of the firft fpecies are, in this
refpect, extremely limited. You know that with
the aftrOnomical telefcope, the magnifying power has
been carried beyond two hundred times, which gives
them an inconceivable fuperiority over thofe of the
firft fpecies, which can fcarcely magnify ten times ;
and the trifling inconvenience of the inverted po~
fition is infinitely overbalanced by an advantage fo
very great.
I will endeavour to put this important article in
the cleareft light poflible.
i. The object E e (plate VIII. Jig. ii.) being infi-
nitely diftant, let e be it's extremity, ftill vifible
through the telefcope, whofe lenfes are PAP and
O B Q, fitted on the common axis E A B O, it falls
to be attentively confidered what direction will be
purfued by the fmgle ray which panes from the ex-
tremity e of the object, through the centre A of the
objective lens; You will recollect that the other
rays, which fall from the point e on the objective
lens only accompany and ftrengthen the ray in quef-
tion e A, which is the principal with refpect to viiion.
i. Now this ray e A, pafiing through the centre
B b 4 of
37^ OF THE APPARENT FIELD, AND
&f the lens P P, will undergo no refraction, but will
purfue it's direction in the ftraight line Af ni, and
palling through the extremity of the image F/will
fall on the ocular lens at the point m ; and here it is
to be obferved, that if the fize of the ocular lens had
not extended fo far as the point ;«, this ray would
never have reached the eye, and the point e would
have been invifible. That is to fay, it would be ne-
ceffary to take the extremity e nearer to the axis, in
order that the ray Afm may meet the ocular lens.
3. Now this ray A m will be refracted, by the ocu-
lar lens, in a way which it is very eafy to difcover.
We have only to confider the fecond image G g,
though infinitely diftant, it is fumcient to know that
the ftraight line Bf produced will pafs through the
extremity g of the fecond image G g, which is the
immediate object of vifion. Having remarked this^
the refracted ray mufl alTume the direction ?i O, and
this produced panes through g.
4. As, therefore, the two lines O n and Bf meet
at an infinite diftance at g, they may be conlidered
as parallel to each other ; and hence we acquire an
eafier method to determine the pofition of the re-
fracted ray n O : you have only to draw it parallel
to the line B/.
5. Hence it is clearly evident that the ray n O will
fomewhere meet the axis of the telefcope at O, and
as ufualiy, when the magnifying power is great, the
'point F is much nearer to the lens Q Q than to the
lens P P, the diftance B m will be fomewhat greater
than
THE PLACE OF THE EYE, y-'J
than the image F/: and as the line n O is parallel to
/ B, the line B O will be nearly equal to B F, that is,
to the focal diftance of the ocular lens.
6. If, then, the eye is placed at O, it will receive
not only the rays which proceed from the middle of
the object. E, but thofe likewife which proceed from
the extremity <?, and confequently, thofe alfo which
proceed from every point of the object ; the eye
would even receive at once the rays B O and n O,
even fuppoiing the pupil infinitely contracted. In
this cafe, therefore, the apparent field does not de-
pend on the largenefs of the aperture of the pupil,
provided the eye be placed at O, but the moment it
recedes from this point, it muft lofe conflderably in
the apparent field.
7. If the point m were not in the extremity of the
ocular lens, it would tranfmit rays ftill more remote
from the axis, and the telefcope would, of courfe, dis-
cover a larger field. In order then, to determine
the real apparent field which the telefcope is capable
of difcovering, let there be drawn, from the centre
A of the objective lens, to the extremity in of the
ocular, the ftraight line A m, which, produced to the
object, will mark at e the vifible extremity ; and
confequently the angle E A <?, or, which is the fame
thing, the angle B A m, will give the femi-diameter
of the apparent field, which is, confequently, greater
in proportion as the extent of the ocular lens is
greater.
8. As, then, in the flrlt fpecies of telefcopes, the
apparent field depended entirely on the aperture of
the
378 OF THE PLACE OF THE EYE.'
the pupil, and as in this cafe it depends entirely ori
the aperture of the ocular lens, there is an effential
difference between thefe two fpecies of inftruments,
greatly in favour of the latter. The figure which I
have employed in demonftrating this laft article, re-
fpecting the place of the eye and the apparent field,
may greatly aflift in the elucidation of the preceding
articles.
If you will.be fa good as to reflect., that the ob-
jective lens tranfports the object E e to ¥f, and that
the ocular lens tranfports it from F/"to Gg; this
image G g being very diftant from the immediate
obje£t of vifion, ought to be feen diftinctly, as a good
eye requires a great diftance in order to fee thus.'
This was the firft article.
As to the fecond, it is evident at firft fight, that
as inftead of the real image E e we fee through the
telefcope the image G g, it muft be inverted. Finally,
this image is feen by the eye placed at O under the
angle G O g, or BO n, whereas the object itfelf E e
appears to the naked eye under the angle E A e .- the
telefcope, therefore, magnifies as many times as the
an^le B O n is greater than the angle E A a Now,
as the line n O is parallel to Bf the angle B O n is
equal to the angle FB/, and the angle E Ae is equal
to it's oppofite and vertical angle F Af; hence the
magnifying power muft be eftimated from the pro-
portion between the angles F Bf and F Af; accord-
ingly, as the angle F Bf contains the angle F Af as
often as the line A F, that is the focal diftance of the
objective lens, contains the line B F, that is the focal
diftance
ASTRONOMICAL TELESCOPES. 7>79
diftance of the ocular, the magnifying power will be,
therefore, expreffed by the proportion of thefe two
diftances. This is proof fufficient that the elements
of geometry may be fuccefsfully employed in re-
fearches of quite a different nature j a reflection not
unpleafing to the mathematician.
x^d February, 1762.
LETTER XCV.
Determination of the magnifying Power of Aflronomical
Telefcopes, and the GonfkruBion of a Telefcope which
Jhall magnify Objecls a given Number of Times.
YOU now have it clearly afcertained, not only
how many times a propofed inftrument will
magnify, but what is the mode of conftructing a te-
lefcope which {hall magnify as many times as may
be wiftied. In the firft cafe, you have only to mea-
sure the focal diftance of both lenfes, the objective as
well as the ocular, in order to difcover how much the
one exceeds the other. This is performed by divi-
fion, and the quotient indicates the magnifying
power.
Having, then, a telefcope the focal diftance of whofe
objective lens is two feet, and that of the ocular one
inch ; it is only neceffary to enquire how often one
inch is contained in two feet. Every one knows that
a foot contains twelve inches, two feet, accordingly,
contain twenty-four inches, which are to be divided
by one. But, whatever number we divide by one,
the
3$0 MAGNIFYING POWER OF
the quotient is always equal to the dividend ; if theM
it is alked, how often one inch is contained in twenty-
four inches, the anfwer, without hefitation, is,twenty-
four times ; confequently, fuch a telefcope magnifies
twenty-four times, that is, reprefents diftant objects
in the fame manner as if they were twenty-four times
greater than they really are ; in other words, you
would fee them through fuch telefcope under an
angle twenty-four times greater than by the naked
eye.
Let us fuppofe another aftronomical telefcope, the
focal diftance of whofe objective lens is thirty-two
feet, and that of the ocular three inches. You fee at
once that thefe two Ienfes mull be placed at the dif-
tance of thirty-two feet, and three inches from each
other, for, in all aftronomical telefcopes, the diftance
of the Ienfes mull be equal to the fum of the two
focal diflances, as has been already demonftfated.*
To find, then, how many times a telefcope of the
above defcription magnifies* we mull divide thirty-
two feet by three inches, and, in Oi*der to this, reduce
thefe thirty-two feet into inches, by multiplying
them by twelve*
32 this produces 384 inches; and thefe again
1 2 divided by three, the focal diftance, in inches^
3)384 of the ocular lens, gives a quotient of 128,
128 which indicates that the propofed telefcope
magnifies ii8 times, which mull be allowed to be
very confiderable;
Reciprocally, therefore, in drder td conftru<5l a te-
lefcope which fhall magnify a given number of times,
fay
ASTRONOMICAL TELESCOPES. 38$
fay 100, we muft employ two convex lenfes, the focal
diftance of the one of which fhall be i oo times greater
than that of the other ; in this cafe the one will give
the objective lens, and the other the ocular. Thefe
muft afterwards be fitted on the fame axis, fo that
their, diftance fhall be equal to the fum of the two
focal diftances ; that is, they muft be fixed in a tube
pf this length, and then the eye being placed behind
the ocular lens, at it's focal diftance, will fee objects
magnified 100 times.
This arrangement may be varied without end, by
affuming an ocular lens at pleafure, and adapting to
it an objective, whofe focal diftance iliall be 100 times
greater. Thus, taking an ocular lens of one inch
focus, the objective muft be of ioo inches focus, and
the diftance of the lenfes 101 inches. Or, taking an
ocular of 2 inches focus, the objective muft have it's
focus at the diftance of 200 inches, and the diftance
pf the lenfes will be 202 inches. If you were to take
an ocular lens of 3 inches focus, the focal diftance of
the objective muft be 300 inches, and the diftance of
the lenfes from each other 303 inches. And if you
were to take an ocular lens of 4 inches focus, the ob-
jective muft have a focal diftance of 400 inches, and
the diftance of the two lenfes 404 inches, and fo on,
the inftrument always increafing in length. If, on
the contrary, you were to affume an ocular lens of
only half an inch focus, the objective muft have a
focal diftance of 100 half inches, that is, of fifty ir :hes,
and the diftance between the lenfes would only .■* 50
inches and a half, which is little more than &•& 3eti
And
382 ASTRONOMICAL TELESCOPES.
And if an ocular of a quarter, of an inch focus were
to be employed, the objective would require a focal
diftance of only too quarters of an inch, or 25 inches,
and the diftance between the two lenfes 25 inches
and a quarter, that is little more than two feet.
Here, then, are feveral methods of producing the
fame effect, that of magnifying 100 times; and if
every thing elfe were equal, we mould not helitate
about giving the preference to the laft, as being the
fhorteft, for here the telefcope, being reduced to little
more than two feet, would be more manageable than
one much longer.
No one, then, would helitate about preferring the
{horteft telefcopes, provided all other circumftances
were the fame, and all the different fpecies reprefented
objects in the fame degree of perfection. But, though
they all poffefs the fame magnifying power, the re-
prefentation is by no means equally clear and diftinct.
That of two feet in length certainly magnifies loo
times, as well as the others ; but on looking through
fuch a telefcope, objects will appear not only dark,
but blunt and confufed, which is undoubtedly a very
great defect. The laft telefcope but one, whofe ob-
jective lens is 50 inches focus, is lefs fubjec*t to thefe
defeats, but the dimnefs and confufion are ftill in-
iuppqrtable :' and thefe defe&s diminifh in proportion
as we employ greater objective Jenfes j and are re-?
duced to almqft nothing, on employing an objective
lens of 306 inches, with an ocular of 3 inches focus,
On increahng thefe meafurements, the reprefentation
becomes itill clearer and more diftind \ fo that, in,
this
DEGREE OF CLEARNESS. 383
this refpeft, long telefcopes are preferable to fhort?
though otherwife Idfs commodious. This circum-
ftance impofes on me a new talk, that of farther ex-
plaining two very effential articles in the theory of
telefcopes : the one refpects the clearnefs, or degree
of light in which objects are feen : and the other the
diftinctnefs and accuracy of expreflion with which
they are reprefented. Without thefe two qualities,
all magnifying power, however great, procures no
advantage for the contemplation of objects.
27 th February, 176a.
LETTER XCVI.
Degree of Clearnefs.
IN order to form a judgment of the degree of
clearnefs in which objects are reprefented by the
telefcope, I fhall recur to the fame principles which I
endeavoured to elucidate, in treating the fame fub-
ject with reference to the microfcope.
And, firft, it muft be confidered that, in this re-
fearch, it is not propofed to determine the degree of
light relident in objects themfelves, and which may
be very different, not only in different bodies, as
being in their nature more or lefs luminous, but in
the fame body, according as circumftances vary. The
fame bodies, when illuminated by the fun, have un-
doubtedly more light than when the Iky is overcaft,
and in the night their light is wholly extinguifhed ;
but
3<54 DEGREE OF CLEARNESS.
but different bodies illuminated may differ greatly,
in point of brightnefs, according as their colours are
more or lefs lively. We are not enquiring, then, into
that light or brightnefs which refides in objects them-
felves ; but, be it ftrong or faint, we fay that a tele-
fcope reprefents the object in perfect clearnefs, when
it is feen through the inftrument as clearly as by the
naked eye ; lb that if the object be dim, we are not
to expect that, the telefcope mould reprefent it as
clear.
Accordingly, in refpect of clearnefs, a telefcope is
perfect, when it reprefents the object as clearly as it
appears to the naked eye. This takes place, as in
the microfcope, when the whole opening of the pupil
is filled with the rays which proceed from every
point of the object, after being tranfmitted through
the telefcope. If a telefcope furnifhes rays fuificient
to fill the whole opening of the pupil, no greater de-
gree of clearnefs need be defired ; and, fuppofing it
could fupply rays in greater profufion, this would be
entirely ufelefs, as the fame quantity precifely, and no
more, could find admiffion into the eye.
Here, then, attention muft be paid chiefly to the
aperture of the pupil, which, being variable, prevents
pur laying down a fixed rule, unlefs we regulate our-
felves according to a certain given aperture, which
is fufncient, when the pupil, in a ftate of the greate$
contraction, is filled with rays ; and, for this purpofe,
the diameter of the pupil is ufually fuppofed to be
one line, twelve of which make an inch $ we fome-
times,
DEGREE OF CLEARNESS. 385
times fatisfy ourfelves with even the half of this, al-
lowing to the diameter of the pupil only half a line,
and in fome cafes flill lefs;
If you will pleafe to confider, that the light of the
fun exceeds that of the moon 300,000 times, though
even that of the moon is by no means inconfiderable*
you will be fenfible that a fmall diminution in point
of clearnefs can be of no great confequence in the
contemplation of objects. Having premifed this, all
that remains is to examine the rays which the tele-
fcope tranfmits into the eyes and to compare them
with the pupil ; and it will be fufficient to confider
the rays which proceed from a fingle point of the ob-
ject (plate IX-jrg. i.J that, for example, which is in
the axis of the telefcope*
I. The object being infinitely diftant, the rays which
fall from it on the furface of the objective lens PAP
are parallel to each other : all the rays, then, which
come from the centre of the object, will be contained
within the lines L P, L P, parallel to the axis E A.
All thefe rays taken together are denominated the
fafcicle of rays which fall on the objective lens, and
the breadth of this fafcicle is equal to the extent or
aperture of the objective lens, the diameter of which
is PAP.
II. This fafcicle, or little bundle, of rays is changed,
by the refraction of the objective lens, into a conical
or pointed figure P F P, and having crofted at the
focus F, it forms a new cone m F ??i, terminated by
the ocular lens ; hence it is evident that the bafis of
this cone m m is as many times fmaller than the
Vol. II. C c breadth
386 DEGREE of CLEARNESS.
breadth of the fafcicle P P, as the diftance F B is
fhorter than the diftance A F.
III. Now thefe rays F m, F m, on palling through
the ocular lens Q B Q, become again parallel to each
other, and form the fafcicle of rays n 0, n 0, which
enter into the eye, and there depict the image of the
point of the object whence they originally proceeded.
IV. The, queftion, then, refolves itfelf into the
breadth of this fafcicle of rays no, n 0, which enter
into the eye j for if this breadth nn or og is equal to,
or greater than., the opening of the pupil, it will be
filled with them, and the eye will enjoy all pofiible
clearnefs ; that is, the objecl will feem as clear as if
you were to look at it with the unaflifted eye.
V. But if this fafcicle n n, or 0 0, were of much lefs
breadth than the diameter of the pupil, it is evident
that the reprefentation muft become fo much more
obfcure ; which would be a great defect in the tele-
icope. In order to remedy it, the fafcicle muft,
therefore,, be at leaft half a line in breadth, and it
would be ftill better to have it a whole line in breadth,
this being the ufual aperture of the pupil.
VI. It is evident that the breadth of this fecond
fafcicle has a certain relation to that of the firft, which
it is very eafy to determine. You have only to fettle
how many times the diftance n n or m m is lefs than
the diftance P P, which is the aperture of the objective
lens. But, the diftance P P is in the fame proportion
' to the diftance m m, as the diftance A F to the diftance
B F, on which the magnifying power depends ; ac-
cordingly, the magnifying power itfelf discovers how
many
APERTURE OF OBJECTIVE LENSES. ^7
many times the fafcicle LP, LP, is broader than the
fafcicle n o, n o, which enters into the eye.
VIL Since, then, the breadth n n or o o mull: be
one line, at leaft half a line, the aperture of the ob-
jective lens PP muft at leaft contain as many half
lines as the magnifying power indicates ; thus, when
the telefcope is to magnify 100 times, the aperture
of it's objective lens muft have a diameter of 100
half lines, or 50 lines, which make 4 inches and 1
lines.
VIII. You fee, then, that, in order to avoid ob-
fcurity, the aperture of the objective lens muft be
greater, in proportion as the magnifying power is
greater. And, confequently, if the objective lens
employed is not fufceptible of fuch an aperture, the
telefcope will be defective in refpect of clear nefs of
reprefentation.
Hence it is abundantly. evident, that, in order to
magnify very greatly, it is impoilible to employ
fmall objectives;, whofe focal diftance is too Ihort, as
a lens formed by the arches of fmall circles cannot
have a great aperture.
\Jl March, 1762.
LETTER XCVIL
Aperture ofObjeclive Lenfes.
YOU have now feen that the magnifying power
determines the fize or extent of the' objective
lens, in order that objects may appear with a fufli-
cient degree of clearnefs. This determination re-
C c 2 fpects
^88 AfcEkTtJRE OF OBJECTIVE LENSES.
fpects only the fize or aperture of the objective lens ;
however the focal diftance is affected by it likewife,
for the larger the lens is, the greater muft be it's
focal diftance.
The reafon of this is evident, as in order to form a
lens whofe focal diftance is, for example, two inches,
it's two furfaces muft be arches of a circle whofe ra-
dius is likewife about two inches : I have therefore
reprefented {plate IX. fig. 2.) two lenfes P and O,
the arches of which are defcribed with a radius of
two inches. The lens P, being the thicker, is much
greater than the lens O ; but I fhall demonftrate after-
wards that thick lenfes are fubjecl: to other inconve-
niencies, and thefe fo great as to oblige us to lay them
altogether afide. The lens Q, then, will be found
more adapted for ufe, being compofed of fmaller
arches of the fame circle ; and as it's focal diftance
is two inches, it's extent or aperture mtz may fcarcely
exceed one inch. Hence this may be laid down as
a general rule, that the focal diftance of a lens muft
always be twice greater than the diameter of it's
aperture m n j that is, the aperture of a lens muft, of
neceftity, be fmaller than half the focal diftance.
Having remarked, then, that in order to magnify
100 times, the aperture of the objective lens muft
exceed 4 inches, it follows, that the focal diftance muft '
exceed 8 inches ; I fhall prefently demonftrate that
the double is not fufficient, and that the focal diftance
of this lens muft be increafed beyond 300 inches.
The diftin&nefs of the expreffion of the image re-
quires this great increafe, as fhall afterwards be
fhewn ; I fatisfy myfelf with remarking at prefent,
that
APERTURE OF OBJECTIVE LENSES. 389
that with regard to the geometrical figure of the
lens, the aperture cannot be greater than half it's
focal diftance.
Here, therefore, I mall go fomewhat more into
the detail, reflecting the opening of the objective,
which every magnifying power requires : and I re-
mark, firft, that though a fufficient degree of clear-
nefs requires an opening of four inches, when the
telefcope is to magnify ioo times, we fatisfy our-
felves, in aftronomical inftruments, with one of three
inches, the diminution of clearnefs being fcarcely
perceptible. Hence artifts have laid it down as a
rule, that, in order to, magnify ioo times, the open-
ing of the objective lens muft be three inches, and
for other magnifying powers in that proportion.
Thus, in order to magnify 50 times, it is fufficient
that the opening of the objective lens be an inch and
a half; to magnify 25 times, three quarters of an
inch fuffice, and fo of other powers.
Hence we fee that for fmall magnifying powers, a
very fmall opening of the objective lens is fuiEcient,
and that, confequently, a moderate focal diftance may
anfwer. But if you wifhed to magnify 200 times,
the opening of the objective muft be fix inches, or
half a foot, which requires a very large lens, whofe
focal diftance muft exceed even ioo feet, in order to
obtain a diftinct and exact expreffion. For this rea-
fon, great magnifying powers require very long te-
lefcopes, at leaft, according to the ufual arrangement
of lenfes which I have explained. But, for fome
time paft, artifts have been fuccefsfully employing
C c 3 themfelves
390 APERTURE OF OBJECTIVE LENSES.
themfelves in diminifhinp- this exceffive length. The
opening of the objective, however, mult follow the
rule laid down, as clearnefs neceffarily depends on it.
Were yon defirous, therefore, of " conftructing a
telefcope which mould magnify 400 times, the open-
ing of the objective lens mud: be twelve inches, or a
foot, let the focal diftance be rendered as fmall as
you will : and if you wifhed to magnify 4,000 times,
the opening* of the objective muft be ten feet, a very
great fize indeed, and too much fo for any artift to
execute ; and this is the principal reafon, why we
can never hope to carry the magnifying power fo
far, unlefs fome great prince would be at the ex-
penfe of providing and executing lenfes of fuch mag-
nitude j and, after all, perhaps, they would not fuc-
ceed.
■ A telefcope, however, which fhould magnify 4,000
times, would difcover many wonderful things in the
heavens. The moon would appear 4,000 times
larger than to the naked eye ; in other words, we
fhould fee her as if {he were 4,000 times nearer to us
than fhe is, . Let us enquire, then, to what a degree
we might be able to diftinguifh the different bodies
which fhe may contain. The diftance of the moon
from the earth is calculated to be 52,000 German
miles j* the 4,000th part of which is 13 miles : fuch
a telefcope would, accordingly, {hew us the moon as
if flie were only 1 3 miles diftant ; and, confequently,
* For the proportion of thefe to meafurement in Englifh miles,
■fee Yol. I. Letter I. page 3,
we
APERTURE OF OBJECTIVE LENSES. 391
we fliould be enabled to difcover in her the fame
things which we diftinguifh in objects removed- to
the fame diftance. Now, from the top of a moun-
tain, we can eafily difcern other mountains more
than 13 miles diftant. There can be no doubt, then,
that, with fuch an inftrument, we mould difcover on
the furface of the moon many things to fill us with
furprize. $iit, in order to determine whether the
moon is inhabited by creatures iimilar to thofe of the
earth, a diftance of 13 miles is ftill too great ; we
mud have, in order to this effect, a telefcope which
fhould magnify ten times more, that is 40,000 times,
and this would require an objective lens of 100 feet
aperture, an enterprize which human art will never
be able to execute. But, with fuch an inftrument,
we fliould fee the moon as if fhe were no farther
diftant than from Berlin to Spandau, and good eyes
might eafily difcern men at this diftance, if any there
were, but too indiftinctly, it muft be allowed, to be
completely aim red of the fact.
As we muft reft fatisfied with wifhing, on this fub-
ject, mine fliould be to have at once a telefcope which
fliould magnify 100,000 times j* the moon would
then appear as if fhe were only half a mile diftant.
The aperture of the objective lens of this telefcope
muft be 250 feet, and we fliould fee, at leaft, the
larger animals which may be in the moon.
ttb March, 1762.
* Dr. Herfchel's telefcopes a&ually magnify 6, $00 times.
Cc4 LETTER
|92 - ON DISTINCTNESS JSjf
LETTER XCV1II.
On Di/iinclnefs in the Exprejfion : Chi the Space of Dif-
fujion occafioned by the Aperture of Objeclme Lenfes %
and confidered as the jirfk Source of Want of Dijlincl-
nefs in tj?e Reprefentdtion.
JSTINCTNESS of expreflion is a quality of fo
much importance in the conftruetion of tele-
fcopes,tthat it feems to take precedence of all the
others which I have been endeavouring to explain j
for it muft be allowed, that a telefcope which does
not reprefent difUnctly the images of objects muft be
very defective. I muft, therefore, unfold the reafons
of this want of diftinclnefs, that we may apply more
fuccefsfully to the means of remedying it.
They appear fo much the more abftrufe, that the
principles hitherto laid down do not difcover the
fource : in fact, this defect, is thus to be accounted
for, one of the principles on which I have hitherto
proceeded is not ftriclly true, though not far from
the truth.
You will recollect, that it has been laid down as a
principle, that a convex iens collects into one point
of the image all the rays which come from one
point of the object. Were this ftrictly true, images
reprefented by lenfes would be as diftinctly expreffed
as the object itfelf, and we fliould be kunder no ap-
preheniiori of defect in regard to this.
Here, then, lies the defectivenefs, of this, principle j
lenfes
THE EXPRESSION, 393
lenfes have the property now afcribed to them only
around their centre ; the rays which pafs through
the extremities of a lens collect in a different point
from thofe which pafs toward the centre, though all
proceed from the fame point of the object ; hence
are produced two different images, which occafiori
mdiftinctnefs.
In order to fet this in the cleared light, let us con-
sider the convex lens P?, (plate IX. Jig. 3. ) on the
axis of which is placed the object E c, of which the
point E, fituated upon the axis, emits the rays, EN,
EM, E A, EM, EN, to the furface of the lens. To
the direction of thefe rays, as changed by refraction,
we muft now pay attention.
J. The ray EA, which panes through the centre
A of the lens, undergoes no refraction, but proceeds
forward in the fame direction, on the ftraight line;
ABF.
II. The rays EM and EM, which are neareft to
the firft, undergo a fmall refraction, by which they
will meet with the axis fomewhere ' at F, which is
the place of the image Ff, as has been explained in
fome of my preceding letters on this fubject.
III. The rays EN and EN, which, are more remote
from the axis E A, and which pafs toward the extre-
mities NN of the lens, undergo a refraction fome-
what different, which collects them, not at the point
F, but at another point G nearer the lens, and thefe
rays reprefent another image Gg, different from the
firft ¥f.
IV. Let us now carefully attend to this particular
circumftance,
394 ON DISTINCTNESS IN
circunrftancej not hitherto remarked ; it is this, that
the rays palling through the lens, toward, it's extre-
mities, reprefent another image G g, than what is
reprefented by thofe pafiing near the centre MAM.
V. If the rays EN, EN, were to retire ftill farther
from the centre A, and to pafs through the points
PP of the lens, their point of re-union would be ftill
nearer to the lens, and would form a new image,
nearer than even G r>
VI. Hence you will eahly perceive, that the firft
image Fy, which is named the principal image, is
formed only by the rays which are almoft infinitely
near the centre ; and that according as the rays re-
tire from it, toward the extremities of the lens, a
particular image is formed nearer the lens, till thofe
pafiing clofe to the extremities form the laft, Gg.
VII. All the rays, therefore, which pafs through
the lens PP reprefent an infinity of images difpofed
between Ff and Gg; and at every diftance from
the axis the refraction of the lens produces a parti-
cular image, fo that the whole fpace between F and G
is filled with a feries of images.
VIII. This feries of images is accordingly deno-
minated the diffufion of the image ; and "when all
thefe rays afterwards enter into any eye, it is natural
that the vifion fnould be fo much difturbed, as the
fpace FG, through which the image is diffufed, is
more confiderable. If this fpace FG could be re-
duced to nothing, no confulion or indiftin chiefs need
to be apprehended.
IX. The greater portions of their refpective circles
that
THE EXPRESSION. 395
that the arches PAP and PBP are, the greater like-
wife is FG the fpace of diffufion. You fee a good
reafon, then, for rejecting all lenfes of too great
thicknefs, or in which the arches which form the
furfaces of the lens are considerable fegments of their
circles ; (as in plate IX. fig. 4.) of which the arches
PAP and PBP are the fourth part of the whole cir-
cumference, fo that each contains 90 degrees ; this
would, confequently, produce an infufferable con-
fufion.
X. The arches, then, which form the furfaces of
a lens, muft contain much lefs than 90 degrees : if
they contained fo much as 60, the diffufion of the
image would be even then infupportable. Authors
who have treated the fubject, admit of 30 degrees
at moil : and fome fix the boundary at 20 degrees.
A lens of this laft defcription is reprefented by jig. 5.
of plate IX. in which the arches PAP and PBP con-
tain only 20 degrees, each being but the eighteenth
part of the whole circumference of it's refDective
circle.
XI. But if this lens were to fupply the place of the
objective in a telefcope, the arches PAP and PBP
muft contain {till many degrees lefs. For, though
the diffufion of the image be perceptible of itfelf, the
magnifying power multiplies it as many times as the
object is. Therefore, the greater the magnifying
power propofed, the fewer muft be the number of
degrees, which the furfaces of the lens contain.
XII. When the telefcope is intended to magnify
j 00 times, you will recollect, that the aperture of
6 the
396 DIMINUTION OF THE
the objective lens mull be 3 inches, and it's focal
diftance 360 inches, which is equal to the radii with
which the two arches PAP and PBP are defcribed ;
hence it follows that each of theft two1 arches con-
tains but half a degree ; and it is diftinctnefs of ex-
preffion which requires an arch fo fmall. If it were
intended to magnify 200 times, half a degree would
be ftill too much, and the meafure of the arch, in
that cafe, ought not to exceed the third part of a
degree. This arch, however, muft receive an ex-
tent of 6 inches ; the radius of the circle muft, there-
fore, be fo much greater, and confequently, alfo the
focal diilance. This is the true reafon why great
magnifying powers require telefcopes of fuch consi-
derable length.
■gtb March, 176a.
LETTER XCIX.
Diminution of the Aperture of Lenfes, and other Means
of lejfening the Space of Diffiifwn, till it is reduced fa
nothing.
7HEN the fpace of an objective lens is too
great to admit of diftinchiefs of expreflion,
it may be very eafily remedied : you have only to
cover the lens with a circle of pafteboard, leaving
an opening in the centre, fo that the lens may tranf-
jriit no other rays, but thofe which fall upon it
through the opening, and that thofe which before
pafied through the extremities of the lens may be ex^
eluded $
APERTURE OF LENSES. 397
eluded ; for as no rays are tranfmitted but through
the middle of the lens, the fmaller the opening is, the
fmaller likewife will be the fpace of diffufion. Ac-
cordingly, by a gradual diminution of the opening,
the fpace of diffufion may be reduced at pleafure.
Here the cafe is the fame as if the lens were no
larger than the opening in the pafteboard, thus the
covered part becomes ufelefs, and the opening de-
termines the fize of the lens ; this then is the remedy
employed, to give objective lenfes any given extent.
PP is the objective lens {plate IX. Jig. 6.) before
which is placed the pafteboard NN, having the open-
ing M M, which is now the extent of the lens. This
opening MM is here nearly the half of what it
would be, were the pafteboard removed ; the fpace
of diffufion is, therefore, much fmaller. It is re-
marked, that the fpace of diffufion, in this cafe, is
only the fourth part of what it was before. An
opening M M, reduced to a third of P P, would ren-
der the fpace of diffufion nine times lefs. Thus the
effect of this remedy is very confiderable ; and on
covering the extremities of the lens ever fo little, the ;
effect of it becomes perceptible.
If, therefore, a telefcope labours under this defect,
that it does not reprefent objects fufficiently diftinct,
as a feries of images blended together muft of ne-
ceffity produce confufion, you have only to contract
the aperture of the objective lens by a covering of
pafteboard fuch as I have defcribed, and this confu-
fion will infallibly difappear. But a defect equally
embarrafling
39§ DIMINUTION OF THE
embarrafling is the confequence, the degree of bright-
neft is diminimed. You will recollect that every
degree of the magnifying power requires a certain
aperture of the objective lens, that as many rays may
be tranfmitted as are neceffary to procure a fufficient
illumination. It is vexatious, therefore, in curing
one defect, to fall into another ; and in order to the
conftruction of a very good telefcope, it is abfolutely
neceffary that there mould be fufficient brightnefs of
illumination, without injuring diftinctnefs in the re-
prefentation. •
But can there be no method of diminiihmg, nay
of totally reducing, the fpace of diffufion of objective
lenfes, without diminiihing the aperture ? This is the
great enquiry which has for fome time paft engaged
the attention of the ingenious, and the folution of
which promifes fuch a field of difcovery in the fcience
of dioptricks. I mail have the honour, at leaft, of
laying before you, the means which fcientific men
have fuggefted for this purpofe.
As the focus of the rays which pafs through the
middle of a convex lens is more diftant from the
lens, than the focus of the rays which pais through
the extremities, it has been remarked. that concave
lenfes produce a contrary effect. This has fuggefted
the enquiry, whether it might not be pofiible to com-
bine a convex with a concave lens in fuch a manner,
that the fpace of difmfion mould be entirely annihi-
lated ; while, in other refpects, this compound lens
mould produce the fame effect as an ordinary iimple
objective ?
APERTURE OF LENSES. 399
objective ? You know that concave lenfes are mea-
fured by their focal diftance as well as thofe which
are convex j with this difference, that the focus of
the concave is only imaginary, and falls before the
lens, whereas the focus of convex lenfes is real, and
falls behind them. Having made this remark, we
reafon as follows :
I. If we place (plate IX. fg. 7.) behind a convex
lens P A P, a concave one OBOof the fame focal
diftance, the rays which the convex lens would col-
lect in it's focus will be refracted by the concave, fo
that they will again become parallel to each other, as
they were before pafling through the convex lens.
II. In this cafe, therefore, the concave lens deftroys
the effect of the convex, and it is the fame thing as
if the rays had proceeded in their natural direction,
without undergoing any refraction. For the con-
cave lens having it's focus at the fame point F, re-
ftores the paralielifm of the rays, which would other-
wife have met at the point F.
III. If the focal diftance of the concave lens were
fmaller than that of the convex, it would produce a
greater effect, and would render the rays divergent,
as in fig. 8. of plate IX : the incident parallel rays
L M, E A, L M, panning through the two lenfes,
would affume the directions N O, B F, N O, which
are divergent from each other. Thefe twro lenfes
together produce, therefore, the fame effect as a
fimple concave lens, which would imprefs on the
incident parallel rays the fame divergence. Two
fuch lenfes joined together, of which the concave has
a fmaller
40b , APERTURE OF LENSES. i
a fmaller focal diftance than the convex, are there-
fore equivalent to a fimple concave lens. .
IV. But if the concave lens O Q (plate IX. jig. 9.)
has a greater focal diftance than the convex lens P P,
it is not even fufficient to render parallel to each
other the rays which the convex lens by itfelf would
collect, in it's focus F : thefe rays, therefore, continue
convergent, but their convergence will be diminifhed
by the concave lens, fo that the rays, inftead of meet-
ing in the point F, will meet in the more diftant
point O.
V. Thefe two lenfes joined together will produce,
then, the fame effect, as a fimple convex lens which
fliould have it's focus at O, as it would collect the
.parallel rays L M, E A, L M, equally in the fame
point. It is therefore evident that two lenfes may
be combined an infinite variety of ways, the one be-
ing convex and the other concave, fo that their com-
bination {hill be equivalent to a given convex lens.
VI. Such a double objective lens may, therefore,
be employed in the conftruction of telefcopes, inftead
of the fimple to which it is equivalent ; and the ef-
fect, as to the magnifying power, will be juft the
fame. But the fpace of diffufion will be quite dif-
ferent, and it may happen to be greater or lefs than
that of a fimple objective, and in this laft cafe, the
double objective will be greatly preferable to the
-fimple.
VII. But farther, it has been found poffible to ar-
range two fuch lenfes fo that the fpace of diffufion is
reduced abfolutely to nothing, which is, undoubt-
edly,
COMPOUND OBJECTIVE LENSES. 40I
edly, the greatefl advantage pomble in the conftruc-
tion of telefcopes. Calculation enables us to deter-
mine this arrangement, but no artift has hitherto
been found capable of reducing it to practice.
13//6 March, 1762.
LETTER C.
Of Compound Objective Lenfes*
THE combination of two lenfes, of which I have
now given the idea, is denominated a com-
pound objective : the end propofed from them is,
that all the rays, as well as thofe which pafs through
the extremities of a lens, as thofe which pafs through
the middle, fhould be collected in a fmgle point, fo
that only one image may be formed, without diffu-
iion, as in hmple objectives. Could artifts fuceeed
in effecting fuch a conflruction, very great advan-
tages would refult from it, as you {hall fee.
It is evident, firft, that the reprefentation of ob-
jects muft be much more diftinct, and more exactly
exprelfed, as vifion is not difturbed by the apparition
of that feries of images which occupy the fpace of
diffulion, when the objective is mnple.
Again, as this fpace of difrufion is the only reafon
which obliges us to give to fimple objectives fuch an
exceffive focal diftance, in order to render the incon-
venience refulting from it imperceptible ; by em-
ploying compound objectives we are relieved from
that cumberfome expedient, and are enabled to con-
.01. II. Dd ftrucV
402 OF COMPOUND OBJECTIVE LENSES.
ftru& telefcopes incomparably fhorter, yet poffeffing
the fame magnifying power.
When, employing a iingle objective, you want to
magnify a hundred times, the focal diftance cannot
be lefs than thirty feet, and the length of the tele-
fcope becomes ftill greater on account of the ocular
lens, whofe focal diftance muft be added ; a fmall
objective would produce, from it's greater fpace of
diffafion, an intolerable confufion. But, a length of
thirty feet is not only very incommodious, but ar-
tifts feldom fucceed in forming lenfes of fo great a
focal diftance. You will readily perceive the reafon
of this : for the radius of the furfaces of fuch a lens
muft likewife be thirty feet, and it is very difficult to
defcribe exactly fo great a circle, and the flightefl
aberration renders all the labour ufelefs.
Accidents of this fort are not to be apprehended
in the conftruction of compound objective lenfes9
which may be formed of fmaller circles, provided
they are fufceptible of the aperture which the mag-
nifying power requires. Thus, in order to magnify
one hundred times, we have feen that the aperture
of the objective lens muft be three inches ; but it
would be eafy to conftruct a compound objective
whofe focal diftance fhould be only one hundred
inches, and which could admit an aperture of more
than three inches : therefore, as the focal diftance of
the ocular muft be one hundred times fmaller, it
would be one inch ; and the interval between the
lenfes being the fum of their focal diftances, the
length of the telefcope would be only one hundred
and
OF COMPOUND OBJECTIVE LENSES. 403
and one inches, or eight feet five inches, which is far
fhort of thirty feet.
But it appears to me, that a compound objective,
whofe focal diftance mould be fifty inches, might
eafily admit an aperture of three inches, and even
more : taking then an ocular of half an inch focus,
you will obtain the fame magnifying power of one
hundred times, and the length of the telefcope will
be reduced one half, that is to four feet and lefs than
three inches. Such a telefcope, then, would produce
the fame effect as a common one of thirty feet, which
is affuredly carrying it as far as need to be wifhed.
If fuch a compound objective could be made to
anfwer, you would only have to double all thefe
meafurements in order to have one which mould ad-
mit an aperture of fix inches, and this might be em-
ployed to magnify two hundred times, making ufe
of an ocular of half an inch focus, as the two hun-
dredth part of the focal diftance of the objective,
which would, in this cafe, be one hundred inches.
Now, a common telefcope which fhould magnify two
hundred times, muft exceed one hundred feet in
length ; whereas this one, which is conftru6ted with
a compound objective, is reduced to about eight feet,
and is perfectly accommodated to ufe, whereas a te-
lefcope of one hundred feet long would be an un-
wieldy and almoft ufelefs load.
The fubjecT: might be carried ftill much farther,
and by again doubling the meafurements, we might
have a compound obje6tive whofe fxeai diftance
fhould be two hundred inches, or fixteen feet eight
Dd: inches.
404 COMPOUND OBJECTIVE LENSES.
inches, which fhould admit of an aperture of twelve
inches or one foot : taking, then, an ocular of half
an inch focus, as two hundred inches contain four
hundred half inches, we fhould have a telefcope ca-
pable of magnifying four hundred times, and ftill
abundantly manageable, being under feventeen feet ;
whereas were we to attempt to produce the fame
magnifying power with a fimple objective lens, the
length of the telefcope niuft exceed three hundred
feet, and confequently could be of no manner of ufe,
on account of that enormous fize.
They have at Paris a telefcope one hundred and
twenty feet long, and one at London of one hundred
and thirty feet ; but the dreadful trouble of mount-
ing, and pointing them to the object, almoft annihi-
lates the advantages expected from them. From this
you will conclude of what importance it would be
to fucceed in the conftruction of the compound lenfes
which I have been defcribing. I fuggefted the firft
idea of them feveral years ago, and fince then, artifts
of the great eft ability in England and France haTe
been attempting to execute them. Repeated efforts,
and lingular fkill, in the artift, are undoubtedly re-
quisite. Indeed, I have made, with the affiftance of
an able mechanician of our Academy, fome not un-
fuccefsful attempts, but the expence attending fuch
an enterprize has obliged me to give it up.
But the Royal Society of London laft year an-
nounced, that an eminent artift, of the name of Dol-
lond, had fortunately fucceeded ; and his telefcopes
are now univerfaHy admired. An able artift of Paris,
named
SIMPLE OBJECTIVE LENSES. 405
named Paffament, boafts of a fimilar fuccefs. Botli
thefe gentlemen did me the honour, fome time ago,,
to correfpond with me on the fubjecl ; but as the
point in queftion was chiefly, how to furmount cer-
tain great difficulties in the practical part, which I
never attempted, it is but fair that I fhould relinquish
to them the honour of the difcovery. The theory
alone is my province, and it has coft me much pro-
found refearch, and many painful calculations, the
very light of which would terrify you. I fhall there-
fore take care not to perplex you farther with this
abftrufe enquiry.
16 tb March, 1762.
LETTER CI.
Formation of Simple Objective Lenfcs.
IN order to give you fome idea of the refearches
which led me to the construction of compound
objective lenfes, I muft begin with the formation of
the fimple lens.
Obferve, firft, that the two furfaces of a lens may
be formed in an infinity of different ways, by taking
circles of which the furfaces are fegments, either
equal, or unequal to each other, the focal diftance,
however, remaining always the fame.
The fame figure is ufually given to both furfaces
of a lens, or, as the furfaces of a lens are reprefented
by arches of a circle, both furfaces are formed with
radii equal to each other. Facility of execution has,
D d 3 undoubtedly,
406 FORMATION OF
undoubtedly, recommended this figure, as the fame
bafon ferves to form both furfaees, and moft artifts
are provided with but few bafons.
Suppofe, then, a convex lens, both whofe furfaees
are polifhed on the fame bafon, one of twenty-four
inches radius, fo that each furface fliall be an arch of
the circle whofe radius is twenty-four inches : this
lens will be convex on both fides, and will have it's
focal diftance at twenty-four inches, according to the
common calculation ; but as the focus depends on
the refraction, and as the refraction is not abfolutely
the fame in every fpecies of glafs, in which we find
a very confiderable diverfity, according as the glafs
is more or lefs white and hard, this calculation of
the focus is not ftrictly accurate ; and ufually the
focal diftance of the lens is fomewhat lefs than the
radius of it's two furfaees, fometimes the tenth part,
fometimes the twelfth ; accordingly, the lens fup-
pofed, the radius of whofe furfaees is twenty-four
inches, will have^ it's focus at the diftance of about
twenty-two inches, if it is formed of the fame fpecies
of glafs of which mirrors are commonly manufac-
tured ; though even in glafs of this fort we meet
with a fmall diverfity in refpecl of refraction.
We fee afterwards that on making the two fur-
faces of the lens unequal, an infinity of other lenfes
may be formed, which fhall all have the fame focal
diftance ; for on taking the radius of one of the fur-
faces lefs than twenty-four inches, that of the other
fu.rface muft be taken greater in proportion, accord-
ng to a certain rule. The radius of one of the fur-
faces
SIMPLE OBJECTIVE LENSES. 407
faces may always be taken at pleafure ; and by means
of a certain rule, the radius of the other maybe found,
in order that the focal diflance may become the fame
as if each furface had been formed on a radius of
twenty-four inches. The following table exhibits
feveral fuch lenfes, which have all the fame focal
diftance.
Radii of the firft
' Radii of the fecond
Lenfes.
Surface.
Surface.
I.
24
24
II.
21
28
III.
20
3°
IV.
18
36
V.
16
48
VI.
15
60
VII.
14
84
VIII.
J3
. 156
IX.
12
infinity.
In the laft form, the radius of one furface is only
1 2 inches, or the half of 24 inches, but that of the
other becomes infinite ; or rather, this furface is an
arch of a circle infinitely great ; and as fuch an arch
differs nothing from a ftraight line, this may be con-
fidered as a plane furface, and fuch a lens is plano-
convex.
Were we to aflume the radius of a furface flill
fmaller than 12 inches, the other furface muft be
made concave, and the lens will become convexo-
Dd 4 concave j
4o8
FORMATION OF
concave ; it will, in that cafe, bear the name of me-
nifciis, feveral figures of which are prefented in the
following table.
Radius of the Convex
Radius of the Concave
Meriifcus.
Surface.
Surface.
X.
II
J3*
XL
IO
6o
XII.
9
3*
XIII.
3
24
XIV.
6
12 . '
XV.
4
6
. XVI.
3
4
Here, then, is a new fpecies of lenfes, the laft of
which is reprefented in Jig. 1 1 of plate IX. fo that we
have now 1 6 different fpecies, which have all the
fame focal diftance ; and this is about 22 inches, a
little more or lefs, according to the mature of the
glafs.
When, therefore, the only queftion is, What focal
diftance the lens ought to have ? it is a matter of in-
difference according to which of thefe forms you go
to work : but there may be a very great difference in
the fpace of diffufion, to which each fpecies is fub*
jeered, this fpace becoming fmaller in fome than in
others. When a fimple objective lens is to be em-
ployed, as is ufually done, it is by no means indifferent
of what figure you affume it, for that which produces
the fmalleft fpace of diffufion is to be preferred. Now,
this
SIMPLE OBJECTIVE LENSES. 409
this excellent property does not belong to the firft
fpecies, where the two furfaces are equal ; buj: nearly
to fpecies VII. which polfeffes the quality, that when
you turn toward the object it's more convex furface,
or that whofe radius is fmalleft, the fpace of diffufion
is found to be about one half lefs, than when the
lens is equally convex on both fides: this, therefore,
is the moll advantageous figure for fimple objective
lenfes, and practitioners are accordingly agreed in thg
ufe of it.
It is evident, then, that in order to afcertain the
fpace of diffufion of a lens, it is not fufficient to know
it's focal diftance, it's fpecies likewife mull be deter-
mined, that is, the radii of each furface, and you mult
carefully diftinguifti which fide is turned to the ob-
ject.
After this explanation, pleafe to remark, that in
order to difcover the combination of two lenfes which
mall produce no diffufion of image, it is abfolutely
necelfary to take into the account the figure of both
furfaces of each glafs, and to refolve the following
problem, What muft be the radii of the furfaces of two
lenfes , in order to reduce to tioih'mg the fpace of diffufion ?
The folution requires the moft profound refearches
of the moft fublime geometry ; and fuppofing thefe
to have been fuccefsful, the artilt has, after all, many
. difficulties to furmount. The bafons muft have pre-
cifely that curve which the calculation indicates ; nor
is that fufficient, for in the operation of forming the
lens on the bafon, the bafon fuffers from the friction
in it's turn j hence it becomes necelfary to rectify it's
figure
41 0 DEFECT OF REPRESENTATION
figure from time to time, with all poffible accuracy,,
for if all thefe precautions are not ftrictly obferved,
it is impoffible to enfure fuccefs j and it is no eafy
matter to prevent the lens from affuming a figure
fomewhat different from that of the bafon in which
it is moulded. You muft be fenfible, from all this,
how difficult it muft be to carry to perfection this
important article in dioptricks.
20tb March, 1762.
LETTER CII.
Second Source ofDefecl, as to Dijiinclnefs of Reprefenfa-
tion by the Tele/cope. Different Refrangibility of Rays.
YOU have now feen in what manner it may be
poffible to remedy that defect in lenfes which
airifes from the different refraction of rays, as thofe
which pafs through the extremities of a lens do not
meet in the fame point with thofe which pafs through
it's middle, the effect of which is an infinity of images
difperfed through the fpace of diffufion. But this is
not the only defect; there is another, of fo much
more importance that it feems impoffible to apply a
remedy, the caufe exifting not in the glafs, but in the
nature of the rays themfelves.
You will recollect that there is great variety in
rays, with refpect to the different colours of which
they convey the impreffion. I have compared this
diverfity to that which we meet with in mufical
notes, having laid it down as a principle, that each
2 colour
BY THE TELESCOPE. 411
colour is attached to a certain number of vibrations.
But fuppofing that this explanation mould ftill ap-
pear doubtful, it is beyond all doubt, that rays of
different colours likewife undergo different refrac-
tions in their paffage from one tranfparent medium
to another; thus red rays undergo the leaft refrac-
tion, and violet the greateft, though the difference is
almcft imperceptible. Now, all the other colours, as
orange, yellow, green, and blue, are contained, with
refpect to refraction, within thefe two limits. It
muft likewife be remarked that white is a mixture
of all the colours, which, by refraction, are feparated
from each other.
In fact, when (plate IX. Jig. 12.) a white ray OP,
or a ray of the fun, falls obliquely on a piece of glafs
A B C D, inftead of purfuing it's courfe in the direc^
tion P Q, it not only deviates from this, but divides
into a variety of rays Pr, Pj, Ft, F v: the firft of
which P r, the one that deviates leaft, reprefents the
red colour, and the laft P v, which deviates moft, the
violet colour. The difperfion rv is indeed much
fmaller than it appears in the figure ; the divergence,
however, always becomes more perceptible.
From this different refrangibility of rays, accord-
ing to their different colours, are produced the fol-
lowing phenomena, with refpect to dioptrick glaffes.
I. Let PP (plate IX. fig. 13.) be a convex lens, on
the axis of which O R, at a very great diftance A O,
is the object O 0, the image of which, as reprefented
by the lens, we are to determine, putting afide, here,
the firft irregularity, that which refpects diffufion, or,
which
4'I2 DEFECT OF REPRESENTATION
which amounts to the fame thing, attending to thofe
rays only which pafs through the centre of the lens
A B, as if it's extremities were covered with a circle
of pafteboard.
II. Let us now fuppofe the object O o to be red, fo
that all it's rays ftiall be of the fame nature ; the lens
will fomewhere reprefent the image of it Rr equally
red ; the point R is, in this cafe, denominated the
focus of the red rays, or of thofe which undergo the
leaft refraction.
III. But if the object O o is violet, as rays of this
colour undergo the greateft refraction, the image V v
will be nearer the lens than Rr; this point V is
called the focus of violet rays.
IV. If the object were painted fome other inter-
mediate colour between red and violet, the image
would fall between the points R and V, would be
always very diftinct, and terminated by the ftraight
line o B, drawn from the extremity o of the object,
through the centre of the lens, this being a general
rule for all colours.
V. But if the colour of the object is not pure, as is
the cafe in almoft all bodies ; or if the object is white,
which is a mixture of all colours, the different fpecies
of rays will then be feparated by refraction, and each
will reprefent an image apart. That which is formed
of red rays will be at R r ; and that which is produced
by the violet, at V v; and the whole fpace R V will
be filled with images of the intermediate colours.
VI. The lens PP, then, will reprefent a fucceilion
of images of the object O o difpofed through the
fmall
BY THE TELESCOPE. 413
fmall fpace R V, of which, the mod remote from the
lens, is red, and the neareft V v violet, and the inter-
mediate images of the intermediate colours ; accord-
ing to the order of the colours as they appear in the
rainbow.
VII. Each of thefe images will be abundantly dif-
tinct in itfelf, and all terminated by the ftraight line
0 B v r, drawn from the extremity o of the object
through the centre of the lens B : but they could not
be viewed together, without a very perceptible con-
fufion.
VIII. Hence, then, is produced a new fpace of dif-
fufion, as in the firft irregularity, but differing from
it in this, that the latter is independent on the aper-
ture of the lens, and that each image is painted of a
particular colour.
IX. This fpace of diffufion R V depends on the focal
diftance of the lens, fo as to be always about the
twenty-eighth part; when, therefore, the focal dif-
tance of the lens P P is 28 feet, the fpace R V be-
comes equal to an entire foot, that is, the diftance
between the red image R r and the violet V v is one
foot. If the focal diftance were twice as great, or
56 feet, the fpace R V would be two feet, and fo of
other diftances.
X. Hence, the calculation of the focal diftance of a
lens becomes uncertain, as the rays of each colour
have their feparate focus : when, therefore, the focus
of a lens is mentioned, it is always neceffary to an-
nounce the colour that we mean. But rays of an
intermediate
414 MEANS OF REMEDYING
intermediate nature are commonly underftood, thofe
between red and violet, namely the green.
XL Thus, when it is faid, without farther expla-
nation, that the focal diftance of fuch a lens is 56
feet, we are to underftand that it is the green image
which falls at that diftance ; the red image will fall
about a foot farther off, and the violet a foot nearer.
Here, then, is a new circumftance of eflential im-
portance, to which attention muft be paid in the
conftruction of dioptrical inftruments.
Z^d March, 1762.
LETTER CIII.
Means of remedying this Defecl by compound Objeclives*
IT is neceffary carefully to diftinguifti this new dif*
fufion, or multiplication of the image, arifing from
the different refrangibiiity of rays, as being of dif-
ferent colours from the firft difnifion, occafioned by
the aperture of the lens, in as much as the rays which
pafs through the extremities form another image
than thofe which pafs through it's middle. This
new defect muft, accordingly, be remedied diffe-
rently from the firft.
You will pleafe to recoiled, that I have propofed
two methods for remedying the preceding defect.;
the one confided in an increafe of the focal diftance,
in order to diminiih the curve of the furfaces of the
lens. This remedy introduces inftruments extremely
Ion?-
DEFECTS IN TELESCOPES. 415
long, whenever a great magnifying power is re-
quired. The other confifts in a combination of two
lenfes, the one convex, and the other concave, to mo-
dify the refraction, fo that all the rays, tranfmitted
through thefe lenfes, may meet in the fame point,
and the fpace of diffufion be totally reduced.
But neither of thefe remedies affords tho leaft af-
liftance toward removing the inconvenience arifing
from the different refrangibility of rays. The nrffc
even increafes the evil, for the more that the focal
diftance is increafed, the more confiderable becomes
the fpace through which the coloured images are di£-
perfed. Neither does the combination of two or
more lenfes furnifh any affiftance ; for we are affured
from both theory and experience, that the images of
different colours remain always feparated, however
great the number of lenfes through which the rays
are tranfmitted, and, that the more the lens mag-
nifies, the more the difference increafes.
This difficulty appeared fo formidable to the great
Newton, that he defpaired of finding a remedy for a
defect which he believed abfolutely infeparable from
dioptrical inftruments, when the viiion is produced
by refracted rays. For this reafon he refolved to
give up refraction altogether, and to employ mirrors
inftead of objective lenfes, as reflection is always the
fame for rays of every nature. This idea has pro-
cured for us thofe excellent reflecting telefcopes,
whofe furprizing effects are fo juftly admired, and
which I fhall defcribe after I have explained every
thing relating to refracting inftruments.
On
416 MEANS OF REMEDYING
On being convinced that it was impoffible to re-
medy the different refrangibility of rays, by a combi-
nation of fever al lenfes, I remarked that the reafon
of it was founded on the law of refraction, which is
the fame in every fpecies of glaffes ; and I perceived,
that if it were poffible to employ other tranfparent
fubftances, whofe refraction mould be confiderably
different from that of glafs, it, might be very poffible
to combine fuch fubftance with glafs, in fuch a man-
ner that all the rays mould unite in the formation of
a fingle image, without any fpace of diffufion. In
purfuance of this idea, I found means to compofe
objective lenfes, of glafs and water, wholly exempt
from the effect of the different refrangibility of rays,
which, confequently, would produce as good an ef-
fect as mirrors.
I executed my idea with two menifque, or con*
cavo-convex lenfes, (plate IX. Jig. 14.) the one of
which is A A C C, and the other BBCC, which I
joined together with the concave furfaces toward
each other, filling the void between them with wa-
ter, fo that the rays which entered by the lens
A A G C muft pafs through the water inclofed be-
tween the two lenfes, before they went off through
CCBB. Each ray undergoes, then, four refrac-
tions : the firil on paffing from the air into the lens
A A G C ; the fecond, on paffing from this lens into
the water ; the third on paffing thence into the other
lens CCBB; the fourth, on paffing from this lens
into the air.
As the four furfaces of thefe two lenfes here enter
into
DEFECTS IN TELESCOPES. 4^7
into coiiflderation, I found means to determine their
femidiameters, fo that, of whatever colour a ray of
light might be, after having undergone thefe four
refractions, it fhould re-unite in the fame point, and
the different rcfrangibility no longer produce diffe-
rent images.
Thefe objectives, compounded of two lenfes and
water, were found fubjecl:, at nrft, to the former
defect, namely, that of the rays, which pafs through
the extremities, forming a different focus from what
is formed by thofe which pafs through the middle ;
but, after much painful refearch, I found means to
proportion the radii of the four furfaces in fuch a
manner, that thefe compound objectives became
wholly exempted from the defects of both the clafTes
fpecified. But it was neceffary, to this effect, to
execute fo exactly all the measurements prefcribed.
by the calculation, that the flighteft aberration mult
become fatal to the whole procefs ; I, was, therefore,
obliged to abandon the conftruction of thefe ob-
jectives.
Befides, this project could remedy only the incon-
veniences which affect the objective lens, and the
ocular lens might {till labour under fome defect as
great, which it would be impoffible to remedy in the
fame manner. Several ocular lenfes are frequently
employed in the conftruction of telefcopes, which: I
fhall defcribe afterwards ; we mould not, therefore,
gain much by a too fcrupulous adherence to the ob-
jective only, while we overlook the other lenfes,
Vol. IL E e though
4*8 MEANS OF REMEDYING
though their effect may not be greatly perceptible
relatively to that of the objective.
But, whatever pains thefe researches may have coft
me, I frankly declare, that I entirely give up, at pre-
fent, the contraction of objectives compounded of
glaffes and water ; as well on account of the diffi-
culty of execution, as that I have fince discovered
other means, not of deftroying the effect of the dif-
ferent refrangibility of rays, but of rendering it im-
perceptible. This mall be the fubject of my next
letter.
I'jtb March, tj£z.
LETTER CIV.
Other Means more praclicabie.
INCE the reflecting telefcope came into general
ufe, refracting inftruments have been fo run
down, that they are on the point of being wholly
laid afide. The conftruction of them has, accord-
ingly, for fome time paft, been wholly fufpended,
under a firm perfuafion that every effort to raife
them to a ftate of perfection would be ufelefs, as the-
great Newton had demonftrated that the infurmount-
able difficulties ariling from the different refrangi-
bility of rays, was abfolutely infeparable from the
conftruction of telefcopes.
If this fentiment be well founded, there is no te-
lefcope capable of reprefenting objects, but with a
confufi.cn
DEFECTS IN TELESCOPES. 419
confufion infupportable in proportion to the great-
nefs of the magnifying power. However, though
there are telefcopes extremely defective in this re-
flect, we likewife meet with fome that are excellent,
and nowife inferior to the fo much boafled reflecting
telefcopes. This is, undoubtedly, a very great pa-
radox ; for if this defect really attached to the fub-
ject, we fhould not find a fingle exception. Such an
exception, therefore, and we have the teftimony of
experience that it exifts, well merits every degree of
attention.
We are to enquire, then, how it comes that cer-
tain telefcopes reprefent the object abundantly dif-
tinct ; while others are but too much fubject to the
defect occafioned by the different refrangibility of
rays. I think I have difcovered the reafon, which I
fubmit in the following reflections.
L It is indubitably certain that the objective lens
reprefents an infinity of images of each object, which
are all arranged over the fame fpace of diffufion, and
each of which is painted it's own proper colour, as I
have demonftrated in the preceding Letter.
II. Each of thefe images becomes an object, with
refpect to the ocular lens, which reprefents each fe-
parately, in the colour proper to it , fo that the eye
difcovers, through the telefcope, an infinity of
images, difpofed in a certain order, according to the
refraction of the lens.
III. And if, inftead of one ocular glafs, we were
to employ feveral, the fame thing will always take
place, and inftead of one image, the telefcope will
E e 2 reprefent
420 MEANS OF REMEDYING
reprefent an infinity to the eye, or a feries of images,
each of which expreffes a feparate object, but of a
particular colour.
IV. Let us now coniider {plate IX. fig. 15.) the
laft images prefented, by the telefcope, to an' eye
placed at O ; and let R r be the red image, and V v
the violet, thofe of the other colours being between
thefe two, according to the order of their different
refrangibility. I have not, in this figure, introduced
the lenfes of the telefcope ; the only point, at pre-
fent, being to fliew in what manner the eye fees the
images. Only we muft conceive the diftance of the
eye O from thefe images to be very great.
V. All thefe images R r and V v, with the inter-
mediate, are fituated, then, on the axis of the tele-
fcope O R V, and terminated by a certain ftraight
line, r v, denominated the terrain atrix of all the
images.
VI. As I have reprefented thefe images in the
figure, the red image R r is feen by the eye at O,
under the angle R O r, which is greater than the
angle V O v, under which the violet image V v is
feen. The violet rays which, from the image V v,
enter into the eye, are, therefore, blended with the
red which come from the part R r of the red image
Rr.
VII. Confequently, the eye cannot fee the violet
image without a mixture of rays of other colours,
but which correfpond to different points of the ob-
ject itfclf ; thus the point n of the red image is con-
founded in the eye with the extremity v of the vio-
let
VHJL
JPZaie. TX
DEFECTS IN TELESCOPES. 421
let image, from which a very great confufion mull
arife.
VIII. But the ray r O not being mixed with the
others, the extremity feen will appear red, or the
image will feem bordered with red, which afterward
fuccefiively blends with thefe other colours, fo that
the object will appear with a party-coloured border,
a fault very common in telefcopes, to which fome,
however, are lefs fubject than others.
IX. If the greater image R r were the violet and
V v the red, the confufion would be equally offen-
five, with this difference only, that the extremities of
the object would then appear bordered with violet,
inftead of red.
X. The confufion depends, then, on the pofition
of the terminating ilraight line r v, with relation to
the line VO, and the diverfity which may take place
in it j the refult muft be, that the confufion will be
fometimes greater and fometimes lefs.
XI. Let us now confider the cafe, in which the
laft images, reprefented by the telefcope, are fo ar-
ranged, that the ftraight terminating line v r being
produced, would pafs precifely into the eye. The
eye will then fee (plate IX. fg. 16.) along a fingle
ray vrQ, all the extremities ; and, in general, all the
points which correfpond to one and the fame point
of the object, will be conveyed to the eye by a fingle
ray, and will there, confequently, be distinctly re-
prefented.
XII. Here, then, is a cafe, in which, notwithftand-
jng the diverfity of images, the eye may fee the ob-
E e 3 ject
422 QUALITIES OF A
jed diftinctly, without any confufion of the different
parts, as happened in the preceding cafe. This ad-
vantage, then, will be obtained, when the termi-
nating line v r, being produced, paffes through the
place of the eye O.
XIII. As the arrangement of the laft images R. r
and V v depends on the difpofition of the ocular
lenfes, in order to refcue telefcopes from the defect
imputed to them, nothing more is requifite but to
arrange thefe lenfes in fuch a manner, that the ter-
minating line of the laft images v r fhall pafs through
the eye ; and telefcopes, thus conftructed, will always
be excellent.
^Qih March, 1762.
LETTER CV.
Recapitulation of the Qualities of a good Telefcope.
>N taking a general review of the fubject, you
will readily admit that an excellent telefcope
is a moft valuable commodity, but rarely to be met
with, being, fubject to fo many defects, and fp many
qualities being requifite, each of which has an effen-
tial influence on the conftruction of the inftrument.
As the number of the good qualities is confiderable,
that no one of them may efcape your obfervation, I
fhall again go over the ground, and make a diftinct
enumeration of them.
I, The firft refpects the magnifying power ; and
the more that a telefcope magnifies objects, the more
perfect
GOOD TELESCOPE. 423
perfect undoubtedly it is ; provided that no other
good quality is wanting. Now, the magnifying
power is to be eftimated from the number of times
that the diameter of the object, appears greater than
to the naked eye. You will recolleft that, in tele-
fcopes of two lenfes, the magnifying power is fo
many times greater, as the focal diftance of the ob-
jective lens exceeds that of the ocular. In telefcopes
confiding of more lenfes than two, the determina-
tion of the magnifying power is more intricate.
II. The fecond property of a good telefcope is
brightnefs. It is always very defective when it re-
prefents the object obfcUrely, and as through a mift.
In order to avoid this defect, the objective lens muft
be of fuch a fize as is regulated by the magnifying
power. Artifts have determined that, in order to
magnify 300 times, the aperture of the objective
ought to be three inches diameter, and for every
other magnifying power in proportion. And, when
objects are not very luminous of themfelves, it would
be proper to employ objectives of a ftill greater dia-
meter.
III. The third quality is diftinctnefs or accuracy of
reprefentation. In order to this, the rays which
pafs through the extremities of the objective lens,
ought to meet in the fame point with thofe which
pafs through the middle, or that, at leaft, the aber-
ration fhould not be perceptible. When a fimple ob-
jective'is employed, it's focal diftance muft exceed a
certain limit proportional to the magnifying power.
Thus, if you wifh to magnify 100 times, the fccai
E.e 4 diftance
424 QUALITIES OF A
diftance of the objective muft be at leaft 30 feet. It
is the deftination, therefore, which impofes the ne-
ceility of making telefcopes fo excellively long, if we
want to obtain a very great magnifying power. Now,
in order to remedy this defect, an objective compofed
of two lenfes may be employed; and, could- artifts
fucceed in the contraction of them, we mould be
enabled, very coniiderably, to fhorten telefcopes,
while the fame magnifying power remained. You
will have the goodnefs. to recollect what I have al-
ready fuggefted, at fome length, on this fubject.
IV. The fourth quality regards likewife the dif-
tinclnefs, or purity, of reprefentation, as far as it is
affected by the different refrangibility of rays of dif-
ferent colours. I have fhewn how that defect may
be remedied : and_as it is impomble that the images
formed by different rays, fhould be collected in a
fingle one, the point in queftion is to arrange the
lenfes in the manner I have defcribed in the preced-
ing Letter ; that is, the terminating line of the laft
images muft pafs through the eye. Without this,
the telefcope will have the defecl; of reprefenting ob-
jects furrounded with the colours of the rainbow ;
but the defect will difappear on arranging the lenfes
in the method I have pointed out. But, to this ef-
fect, more than two lenfes muft be employed, in
order to a proper arrangement. I Have hitherto
fpoken only of telefcopes with two lenfes, one of
which is the objective, and the other the ocular; and
you know that their diftance from each other is aL
ready determined by their focal diftances, fo that
here
GOOD TELESCOPE, 425
here we are not at liberty to make any alteration.
It happens, fortunately, however, that the terminat-
ing line, which I have mentioned, panes nearly
through the place of the eye; fo that the defect,
arifins: from the colours of the rainbow, is almoft
imperceptible, provided the preceding defect is re-
medied, efpecially when the magnifying power is
not very great. But when the power is confider-
able it would be proper to employ two ocular lenfes,
in order entirely to annihilate the colours of the rain-
bow : as in this cafe, the ilighteft defects, being
equally magnified, become infupportable.
. V. The fifth and laft good quality of a telefcope,
is a large apparent field, or the fpace which the in-
urnment difcovers at xmce. You recollect that fmall
pocket glaffes, with a concave ocular lens, are fubject
to the defect of prefenting a very fmall field, which
renders them incapable of magnifying greatly. The
other fpecies, that with a convex ocular, is lefs fub-
ject to this defect, but as it reprefents the object in-
verted, telefcopes of the firft fpecies would be pre-
ferable, did they difcover a larger field, which depends
on the diameter of the aperture of the ocular lens ;
and you know we cannot increafe this aperture at
pleafure, becaufe it is determined by focal diftance.
But, by employing two or three, or even more ocu-
lar lenfes, we have found means to render the appa-
rent field greater ; and this is an additional reafon
for employing feveral lenfes, in order to procure a
telefcope in all refpects excellent.
To thefe good qualities, another may be itill added,
that
426 TERRESTRIAL TELESCOPES
that the reprefentation fhall not be inverted by the
inftrument, as by aftronomical telefcopes. But this
defect may be eafily remedied, if it be one, by the
addition of two more ocular lenfes, as I ihall fhew
in my next letter.
3 d April, 1762. '
LETTER CVI.
Terreftrial 'Telefcopes with Four Lenfes.
HAVE treated at coniiderable length of telefcopes
compofed of two convex lenfes, known by the
name of aftronomical tubes, becaufe they are com-
monly ufed for obferving the heavenly bodies.
You will readily comprehend that the ufe of fuch
Inftruments, however excellent they may be, is li-
mited to the heavens, becaufe they reprefent objects
in an inverted pofition, which is very aukward in
contemplating terreftrial bodies, as we would rather
wifh to view them in their natural lituation ; but on -
the difeovery of this fpecies of telefcope, means were
quickly found of remedying that defecl:, by doubling,
if I may fay To, the fame telefcope. For as two lenfes
invert the object, or reprefent the image inverted,
by joining a fimilar telefcope to the former, for view-
ing the fame image, it is again inverted, and this fe-
cond reprefentation will exhibit the object upright.
Hence a new fpecies of telefcopes, compofed of four
'lenfes., called terreftrial telefcopes,from their being de-
figned
WITH FOUR LENSES. 427
figned to contemplate terreftrial objeds : and the
method of conftruding them follows.
I . I. The four lenfes A, B, C, D, (plate IX. Jig. 10.)
inclofed in the tube MMNN, reprcfent the tele-
fcope in queftion ; the firft of which, A, direded to-
ward the object, is denominated the objective lens,
and the other three, BCD, the ocular. Thefe four
lenfes are all convex, and the eye muft be placed at
the extremity of the tube, at a certain diftance from
the laft ocular lens D, the determination of which
fhall be afterwards explained.
II. Let us confider the effect which each lens muft
produce, when the object O o, which is viewed
through the telefcope, is at a very great diftance.
The objective lens will firft reprefent the image of
this object at P p, it's focal diftance, the magnitude
of the image being determined by the ftraight line
drawn from the extremity o, through the centre of
the lens A. This line is not reprefented in the figure,
that it may not be embarraffed with too many lines.
III. This image P p occupies the place of the ob-
ject with refped to the fecond lens B, which is placed
in fuch a manner, that the interval B P fhall be equal
to it's focal diftance, in order that the fecond image
may be thence transported to an infinite diftance, as
Q a, which wri!l be inverted as the firft Pj&, and ter-
minated by the ftraight line, drawn from the centre
of the lens B, through the extremity p.
IV. The interval between thefe two firft lenfes
A B, is equal, therefore, to the fum of their focal dis-
tances j and were the eye placed behind the lens B,
we
428 TERRESTRIAL TELESCOPES
we fhould have an aftronomical telefcope, through
which the object O 0 would be feen at Q q, and,
confequently, inverted, and magnified as many times
as the diftance A P exceeds the diftance B P. But
inftead of the eye, we place behind the lens B, at
fome diftance, the third lens C, with refpect to which
the image Q q occupies the place of the object, as, in
fact, it receives the rays from this image Q q, which,
being at a very great diftance, the lens C will repre-
fent the image of it, at it's focal diftance in R r.
V. The image Q q being inverted, the image R r
will be upright, and terminated by the ftraight line
drawn from the extremity q through the centre of
the lens C, which will pafs through the point r.
Confequently the three lenfes A, B, C together, re-
prefent the object O 0 at R r, and this image R r is
upright.
VI. Finally, we have only to place the laft lens in
fuch a manner that the interval D R fhall be equal
to it's focal diftance ; this lens D will again tranfport
the image R r to an infinite diftance, as S s, the ex-
tremity of which s will be determined by the ftraight
line drawn from the centre of the lens D, through
the extremity r ; and the eye placed behind this lens
will, in fact, fee this image S s, inftead of the real
object O 0.
VII. Hence it is eafy to afcertain how many times,
this telefcope, compofed of four lenfes, muft magnify
the object; you have only to attend to the two
couple of lenfes, A B and C D, each of which, fepa-
rately, would be an aftronomical telefcope. The
firft
WITH FOUR LENSES. 429
firft pair of lenfes A and B magnifies as many times,
as the focal diftance of the firft lens A exceeds that
of the feconds lens B j and fo many times will the
image formed by it, O q, exceed the real object O 0.
VIII. Farther, this image O q occupying the place
of the object, with refpect to the other pair of lenfes
C and D, it will be again multiplied as many times
as the focal diftance of the lens C exceeds that of the
lens D. Thefe two magnifying powers added, give
the whole magnifying produced by the four lenses.
IX. If, then, the firft pair of lenfes A and B mag-
nify ten times, and the other part C and D three
times, Lthe telefcope will magnify the object thrice
ten, that is, thirty times ; and the aperture of the
objective lens A muft correfpond to this magnifying
power, according to the rule formerly laid down.
X. Hence you fee, then, that on feparating from
a terreftrial telefcope the two laft lenfes C and D,
there would remain an aftronomical telefcope, and
that thefe two lenfes C and D would likewife form
fuch a telefcope. A terreftrial telefcope, therefore,
confifts of two aftronomical ; and, reciprocally, two
aftronomical telefcopes combined form a terreftrial.
This conftruction is fufceptible of* endlefs varia-
tions, fome preferable to others, as I fhall afterwards
demonftrate.
6tb Apr V., 1762.
LETTER
43° ARRANGEMENT OF LENSES
LETTER CVIL
. Arrangement of Lenfes hi Terreftrial Tel ef copes,
"\7"OU have now feen how, by the addition of two
-*■ convex lenfes to an aftronomical telefcope, a
terreftrial one is produced, which reprefents the ob-
ject upright. The four lenfes, of which a terreftrial
telefcope is compofed, are fufceptible of an infinite
variety of arrangement, with refpecl: to both focus
and diftance. I fhall explain thofe which are of moft
effential importance, and refer you to plate X-fg' i»
I. With refpecl to their diftances, I have already
remarked, that the interval between the two firft
lenfes A and B is the fum of their focal diftances ;
and the fame thing holds as to the laft lenfes C and
D, for each pair may be confidered as a fimple tele-
fcope, compofed of two convex lenfes. But what
muft be the interval between the two middle lenfes
B and C ? May it be fixed at pleafure ? As it is cer-
tain that, whether this interval be great or fmall, the
magnifying power, always compounded of the two
which each pair would produce feparately, muft con-
tinue the fame.
II. On confulting experience, we foon perceive
that when the two middle lenfes are placed very near
each other, the apparent field almoft entirely va-
nilhes ; and the fame thing takes place when they
are too far feparated. In both cafes, to whatever
2 object
JN TERRESTRIAL TELESCOPES. 43 I
object the telefcope is pointed, we difcover only a
very fmall part of it.
III. For this reafon artifts bring the laft pair of
lenfes nearer to the firft, or remove them to a greater
diftance, till they difcover the largeft field, and delay
fixing the lenfes till they have found this fituation.
Now, they have obferved, that, in fettling this moft
advantageous arrangement, the diftance of the middle
lenfes B and C is always greater than the fum of the
focal diftances of thefe fame two lenfes.
IV. You will readily conclude that this diftance
cannot depend on chance, but muft be fupported by
a theory, and that, affording a termination much
more exa<5t than what experience alone could have
furnilhed. As it is the duty of a natural philofopher
to inveftigate the caufes of all the phenomena which
experience difcovers, I proceed to unfold the true
principles which determine the moil advantageous
diftance B C between the two middle lenfes. For
this purpofe I refer to plate X. Jig. 2.
V. As all the rays muft be conveyed to the eye,
let us attend to the direction of that one which, pro-
ceeding from the extremity o of the vifible object,
paffes through the centre A of the objective lens ;
for unlefs this ray is conveyed to the eye, this extre-
mity 0 will not be. vifible. Now, this ray undergoes
no refraction in the objective lens, for it paffes
through the centre A ; it will therefore proceed in
a ftraight line to the fecond lens, which it will meet
in it's extremity /;, as this is the laft ray transmitted
through the lenfes*
VI. This
432 ARRANGEMENT OF LENSES, &C<
VI. This ray, being refracted by the fecdnd lens^
will change it's direction fo as to meet fomewhere^
at «, the axis of the lenfes ; this would have hap-
pened to be the focus of this lens, had the ray A b
been parallel to the axis ; but as it proceeds from
the point A, it's reunion with the axis at n will be
more diftant fr,om the lens B, than it's focal diftance.
VII. We muft now place the third lens C in fuch
a manner that the ray, after having crofted the axis
at 72, may meet it exactly ,in it's extremity c, from
which it is evident that the greater the aperture of
this lens C is, the farther it muft be removed from
the lens B, and the greater the interval B C becomes 5
but on the other hand, care muft be taken not to
remove the lens C beyond that point, as in this cafe
the ray would efcape it, and be tranfmitted no far-*
ther. This circumftance, then, determines the juft
diftance between the two middle lenfes B and C,
conformably to experience.
VIII. This lens C will produce a new refraction of
the ray in queftion, which will convey it precifely to
the extremity d of the laft ocular lens D, which,
being fmaller than C, will render the line c d fome-
what convergent toward the axis, and will thus un-
dergo, in the laft lens, fuch a degree of refraction as
will reunite it with the axis at lefs than it's focal
diftance ; and there it is exactly that the eye muft
be placed, in order to receive all the rays tranfmitted
through the lenfes, and to difcover the greateft field.
IX. Thus we are enabled to procure a field v/hofe
diameter is almoft twice as large as with an agrono-
mical
CONSTRUCTION OF TELESCOPES. 433
mical telefcope of the fame magnifying power. By-
means, then, of thefe telefcopes, with four lenfes, we
obtain a double advantage, the object is reprefented
.upright, and a much larger field is difcovered : both,
circumftances of much importance.
X. Finally, it is poillble to find fuch an arrange-
ment of thefe four lenfes, as, without affecting either
Of the advantages now mentioned, fhall entirely do
away the defect arifmgfrom the colours of the rain-
bow, and at the fame time reprefent the object with
all poilible diftinctnefs. But few artifts can attain
this degree of perfection.
10th dpril, 1762.
»«*9M><!
LETTER CVIII.
Precautions to be obferved hi the Conjlruclion of Tele-
fcopes. NeceJJtty of blackening the Infide of Tubes,
Diaphragms.
A FTER thefe refearches refpecling the conflruc-
-*- ■*■ tion of telefcopes, I mult fuggeil and explain
certain precautions neceffary to be ufed ; which,
though they relate neither to the lenfes themfelves,
nor to their arrangernent, are neverthelefs of fuch
importance, that if they are not very carefully ob-
ferved, the belt inflrument is rendered entirely ufe-
lefs. It is not 'fuincient that the lenfes mould be ar-
ranged in fuch a manner that all the rays which fall
upon them fhall be tranfmitted through thefe lenfes
to the eye ; care muft be taken, beildes, to prevent
Vol. II. F f the
■1
434 CONSTRUCTION OF TELESCOPES.
the tranfmiffion of extraneous rays through the tele-
fcope, to difturb the reprefentation. Let the follow-
ing precautions, then, be taken.
I. The lenfes, of which a telefcope is compofed,
muft be inclofed in a tube, that no other rays, except
thole which are tranfmitted through the objective,
may reach the other lenfes. For this effect, the tube
muft be very clofe throughout, that not a chink ad-
mit the fmalleft portion of light. If by any accident
the tube fhall be perforated ever fo flightly, the ex-
traneous light admitted would confound the repre-
fentation of the object.
II. It is likewife of importance to blacken, through-
out, the inlide of the telefcope, of the deepeft black
poflible, as it is well known that this colour reflects
not the rays of light, be they ever fo powerful. You
muft have obferved, accordingly, that the tubes of
telefcopes are always blackened internally. A lingle
reflection will fliew the neceffity of it.
HI. The objective lens A, (plate X.Jig. 3.) tranf-
mits not only the rays of the object reprefented by
the telefcope, but thofe alfo which by the extremities
enter all around in great abundance ; fuch is the ray
h a, which falls, on the inlide, upon the frame of the
tube at i : if, therefore, the tube were white in-
wardly, or of any other colour, it would be illumL.
nated by this ray, and of itfelf would generate new
rays of light, which muft of neceffity be conveyed
through the other lenfes, and difturb the reprefenta-
tion by mingling with the proper rays of the object.
IV. But if the infide of the tube be blackened
deeply*
CONSTRUCTION OF TELESCOPES. 435
deeply, no new rays will be produced, let the light
be ever fo ftrong. This blackening muft be carried
through the whole length of the telefcope, as there
is no black fo deep as not to generate, when illu-
minated, fome faint light : fuppofing, then, that
fome extraneous rays were to make their way to the
fecond lens B, the black of the tube, purfuing their
courfe, would eafily abforb them altogether. There
is a brilliant black, which, for this reafon, it would
be very improper to employ.
V. But even this precaution is not fuflicient, it is
necefTary likewife to furnifh the infide of the tube
with one or more diaphragms, perforated with a
fmall circular aperture, the better to exclude all ex-
traneous light ; but care muft be taken that they
exclude not the rays of the obj eel: which the inftru-
ment is intended to reprefent. See plate X.Jig. 4.
VI. It is necefTary to obferve at what place, in the
tube, the proper rays of the object are moft con-
tracted; this muft be at the points where their
images are reprefented, for there all the rays are col-
lected together. Now, the objective lens A repre-
fents the image in it's focus at M. You have only,
then, to compute the magnitude of this image, and
there to fix your diaphragm, whofe aperture m n
fliall be equal to the magnitude of the image, or ra-
ther fomewhat greater. For if the aperture were
lefs than the image, there would be a proportional
lofs of the apparent field, which is always a great
defect.
VII. Thefe are the obfervations, refpecting the
F f 2 diaphragm^
436 CONSTRUCTION OF TELESCOPES.
diaphragm, which apply to aftronomical .telefcopes,
compofed of two convex lenfes. In terreftrial tele-
fcopes two images are reprefented within the tube :
befides the fir ft at M, reprefented by the objective in
it's focus, and which the fecond lens B tranfports to
an infinite diftance, the third lens C reprefents a fe-
cond image in it's focus N, which is upright, where-
as the former was inverted. At N, therefore, is the
proper place to fix a fecond diaphragm perforated
with an aperture n n, of the magnitude of the image
there reprefented.
VIII. Thefe diaphragms, aided by the blacknefs of
the infide of the tube produce likewife an excellent
effect with refpect to diftinclnefs- of reprefentation.
It muft be carefully obferved, however, that the
greater the field is which the telefcope difcovers, the
lefs is to be expected from thefe diaphragms, as in
that cafe the images become greater, fo that the aper-
ture of the diaphragms muft be fo enlarged as to
render them incapable of any longer excluding the
extraneous rays. So much the greater care, there-
fore, muft be taken, thoroughly to blacken the in-
fide of the tube, and to make it larger, which con-
siderably diminiihes the unpleafant effect of which I
have been fpeaking,
i yth April, 1 762.
LETTER
OF TELESCOPES, 437
LETTER CIX.
In what Manner Tele/copes reprefcnt the Moon, the
Planets, the Sun, and the fixed Stars. Why thefe lajl
appear f mailer through the Tele/cope than to the naked
Eye. Calculation of the Dijlance of the fixed Stars,
from a Comparifon of their apparent Magnitude with
that of the Sun,
AM perfuaded that, by this time, you are very
well pleafed, to be relieved, at length, from the
dry theory of telefcopes, which is rendered agreeable
only by the importance of the difcoveries which
they have enabled us to make.
What pleafing furprize is felt on feeing very dif-
tant objects as diftinclly as if they were one hundred
times nearer to us, or more, efpecially in cafes where
there is no poflibility of reaching them, which holds
with refpect to the heavenly bodies ! And you are
already difpofed to admit, that, with the aid of the.
telefcope, many wonderful things relating to the ftars
have been difcovered.
On viewing the moon one hundred times nearer
than fhe really is, many curious inequalities are dif-
cernible ; fuch as exceffive heights and profound -
depths, which, from their regularity, refemble rather
works of art than natural mountains. Hence a very
plaufible argument is deduced, to prove that the moon
is inhabited by reafonable creatures. But we have,
proofs flill more fatisfactory in fimply contemplating
F f 3 the
438 OF TELESCOPES.
the almighty power, in union with the fovereign
wifdom and goodnefs, of the Great Creator.
Thus the moft important difcoveries have been
made refpecting the planets, which, to the unaffifted
eye, appear only as fo many luminous points ; but
which, viewed through a good telefcope, refemble
the moon, and appear even Hill much greater.
But you will be not a little furprized, when I af-
fure you, that with the affiftance of the beft telefcope,
even one which magnifies more than two hundred
times, the fixed liars ftill appear only as points, nay
{till fmaller than to the naked eye. This is fo much
the more aftonifhing, that it is certain the telefcope
reprefents them fuch as they would appear were we
two hundred times nearer. Are we not, hence, re-
duced to the neceffity of concluding that, here-, tele-
fcopes fail to produce their effect ? But this idea pre-
fently vanifhes, on confidering that they difcover to
us millions of little ftars which, without their aid,
mull have for ever efcaped the eye. We likewife
perceive the diftances between the ftars incompa-
rably greater ; for two ftars which, to the naked eye,
feemed almoft to touch each other, when viewed
through the telefcope, are feen at a very confiderable
diftance ; a fufiicient proof of the effect of the tele-
fcope.
What, then, is the reafon that the fixed ftars ap-
pear to us fmaller through the telefcope than to the
naked eye ? In refolving this queftion, I remark, firft,
that the fixed ftars appear greater to the naked eye
than they ought to do, and that this arifes from a
falfe
OF TELESCOPES. 439
falfe light, occafioned by their twinkling. In fact,
when the rays proceeding from a liar come to paint
their image at the bottom of the eye, on the retina,
our nerves are ftruck by it only in one point, but,
by the luftre of the light, the adjacent nerves likewife
undergo a concufllon, and produce the fame feeling,
which would be communicated, if the image of the
object painted on the retina were much greater.
This happens on looking, in the night, at a very dif-
tant light. It appears much greater than when we
view it at a fmall diftance, and this increafe of mag-
nitude is occafioned only by a falfe glare. Now, the
more that a telefcope magnifies, the more this acci-
dent mull diminilh ; not only becaufe the rays are
thereby rendered fomewhat fainter, but becaufe the
real image at the bottom of the eye becomes greater :
fo that it is no longer a fingle point which fupports
the whole impreflion of the rays. Accordingly, how»
ever fmall the liars may appear through a telefcope,
we may confidently affirm, that, to the naked eye*
they would appear Hill much fmaller but for this ac-
cidental falfe light, and that as many times as the
telefcope magnifies.
Hence it follows, that, as the fixed liars appear
only like fo many points, though magnified more
than 200 times, their diftance mull be inconceivable.
It will be eafy for you to form a judgment how this
diftance may be computed. The diameter of the
fun appears under an angle of 32 minutes : if, there-
fore, the fun were 3 2 times farther off, he would ap-
pear under an angle of one minute j and, confer
F f 4 quendy,
44° Of TELESCOPES.
quently, ftill much greater than a fixed ftar viewed
through the telefcope, the diameter of which does
not exceed two feconds, or the thirtieth part of a
minute. The fun, therefore, muft be thirty times
more, that is 960 times, farther removed, before his
appearance could be reduced to that of a fixed ftar
obferved with the afiiftance of a telefcope. But the
fixed ftar is 200 times farther off than the telefcope
reprefents it ; and, confequently, the fun muft be
200 times 960, that is, 192,000 times farther off
than he is, before he could be reduced to the appear-
ance of a fixed ftar. It follows, that if the fixed
ftars were bodies as large as the fun, their diftances
would be 192,000 times greater than that of the fun.
Were they ftill greater, their diftances muft be ftill
fo many times greater ; and fuppofing them even
many times fmaller,- their diftances muft always be:
more than a thoufand times greater than that of the
fun. Now the diftance of the fun from our globe
is about 15,000,000 of German miles.
It is impoilible, undoubtedly, to think of this im-
menfe diftance of the fixed ftars, and of the extent
of the whole univerfe, without aftonifhment. What
muft be the power of that great being who created
this vaft fabric, and who is the abfolute Mafter of it ?
Let us adore Him with the moft profound venera.
tion.
iyb April, ij6z:
LETTER
ELEVATION OF THE MOON, &C. 44X
LETTER CX.
Why do the .Moon, and the Sun, appear greater at rifing
and Jetting, than at a certain Elevation ? Difficulties
attending the Solution of this Phetiomenon.
*OU muft have frequently remarked, that the
mooD, at riling and fetting, appears much
larger than when {he is confiderably above the hori-
zon ; and every one muft give teftimony to the truth
of this phenomenon. The fame obfervation has been
made with refpect to the fun. This appearance has
long been a ftumbling-block to philofophers ; and,
viewed in whatever light, difficulties almoft insupe-
rable prefent themfelves.
It would be ridiculous to conclude, that the moon's
body is really greater, when fhe is in the horizon,
than when fhe has attained her greateft elevation.
For, befides that fuch an idea would be abfurd in it-
felf, it muft be confidered, that when the moon ap-
pears to us in the horizon, fhe appears to other in-
habitants of our globe, more elevated, and conse-
quently fimller. Now, it is impolhble that the fame
body mould be, at the fame time, greater and fmaller.
It would be almoft equally ridiculous to attempt
the folution of this ftrange phenomenon, by fuppoiing
that the moon is nearer to us when Ihe appears in
the horizon, than when me is arrived at a great ele-
vation, from our certain knowledge that a body ap-
pears greater in proportion as it is nearer us ; and
you know that the more diftant any object is, the
fmaller
44-2 ELEVATION OF THE
fmaller it appears. It is for this reafon precifely, that
the ftars appear fo extremely fmall, though their real
magnitude be prodigious.
But however plaufible this idea may feem, it is
totally deftitute of foundation ; for it is undoubtedly
certain, that the moon is at a greater diftance from
us at rifing and fetting, than when at a greater eleva-
tion. The demonftration follows: (plate X.Jig. 5.)
Let the circle ABDbe the earth, and the moon
at L. This being laid down, an. inhabitant at A
will fee the moon in his zenith, or the moil elevated
point of the heavens. But another inhabitant at D,
where the line D L touches the furface of the earth,
will fee the moon at the fame time in his horizon ;
fo that the moon will appear, at the fame inflant, to
the fpectator A in his zenith, and to the other fpec-
tator D in his horizon. It is evident however, that
the laft diftance D L is greater than the firft A L,
and, confequently, the moon is more diftant from
thofe who fee her in the horizon, than from thofe
who fee her near their zenith. Hence it clearly fol-
lows, that the moon, when feen in the horizon, ought
to appear fmaller, being then, in fad, farther from
us, than when arrived at a great elevation. It is
aflonifhing, therefore, that obfervation fhould be in
direct contradiction to this, and that the moon fhould
appear much greater when viewed near the horizon,
than in the fummit of the heavens.
The more this phenomenon is inveftigated, the
more ftrangc it appears, and the more worthy of atten-
tion :• it being undoubtedly certain, that the moon
when
MOON AND THE SUN. 443
when moft remote, that is, in the horizon, ought to
appear fmaller, whereas, neverthelefs, every one is
decidedly of opinion that {he then appears confider-
ably greater. This contradiction is evident, and
even feems to overturn all the principles laid down
in optics, which, however, are as clearly demonftrable
as any in geometry.
I have purpofcly endeavoured to fet this difficulty
in it's ftrongeit light, in order to make you the more
feniible of the importance of the true folution.
Without entering into a difcuilion of this univerfal
judgment formed from appearances, refpecting the
prodigious magnitude of the moon in the horizon, I
fhall confine myfelf to the principal queftion : Is it
true, in facl, that the moon, when near the horizon,
actually appears greater ?
, You know that we are poiTefTed of infallible means
of exactly meafuring the heavenly bodies, by affer-
taining the number of degrees and minutes which
they occupy in the heavens ; or, which amounts to
the fame thing, by meafuring (plate X.Jig. 6.) the
angle EOF, formed by the lines E O and FO,
drawn from the oppolite points of the moon, to the
eye of the fpe&ator O ; and. this angle E O F is what
we call the apparent diameter of the moon. We
have likewife inftruments perfectly adapted to the
purpofe of exactly determining this angle. Now,
when we employ fuch an inftrument in meafuring
the moon's diameter, firft at her riling, and after-
ward, when fhe has gained her greateft elevation, we
actually find her diameter fomewhat lefs in the firft
cafe than in the other, as the inequality of diftance
requires.
444 REFLECTIONS RESPECTING THE
requires. There cannot remain the fhadow of doubt
as to this ; but, for that very reafon, the difficulty,
inflcad of diminiftiing, gathers ftrength ; and it will
be afked with fo much the more eagernefs ; How
comes it that the whole world agrees in imagining
the moon to be greater when rifing or fetting, though
her apparent diameter is then, in reality, fmaller ?
and. What can be the reafon of this dclufion to which
men are univerfally fubject ? The aftronomer, who
knows perfectly well that the moon's apparent dia-
meter is then fmaller, falls neverthelefs into the
lame deception as the moil ignorant clown.
loth April » 1762.
LETTER CXI.
Reflections on the Ouejiion refpc'cling the Moon's appa*
rent Magnitude 7j Progrefs toward a Solution of the
Difficulty. Abfurcl Explanations.
O U would fcarcely have believed, that the
funple appearance of the moon involved fo
many cUilicuIties ; but I hope I fhall be able to clear
the way toward a folution, by the following reflec-
tions.
I. It is not aftonifhing that our judgment refpect-
inp* the magnitude of objects fhould not always be in
corrcfpoD deuce with the vifual angle under which we
fee it : of this, daily experience furnifhes fumcient
proof. A cat, for example, appears, when very near,
under a greater angle than an ox at the diftance of
100 paces. I- could never, at the fame time, imagine
the
MOON3S APPARENT MAGNlTUr.r. 'A,*^ ■
the cat to be larger than the ox : and you will pleafe
to recollect, that our judgment refpecting magni-
tude is always intimately connected with that of dis-
tance ; fo that if v/e commit a miftake in the calcu-
lation of diftance, our judgment refpecting magni-
tude becomes, of neceffity, erroneous.
II. In order to elucidate this more clearly, it fome-
times happens that a fly pailing fuddenly before the
eye, without our thinking of it, if our fight is fixed
on a diftant object, we imagine, at firft, that the fly
is at a great dillance ; and as.it appears under a very
confiderable angle, we take it, for a moment, to be
a large fowl, which, at the proper diftance, would
appear under the fame angle. It is, then, inconteil-
ably certain, that our judgment refpecting the mag-
nitude of objects is not regulated by the vifual angle
under which they are feen, and that there is a very
great difference between the apparent magnitude of
objects, and the calculated or computed magnitude;
The firit. is regulated by the vifual angle, and the
other depends on the diftance to which we fuppofe
the object to be removed.
III. To avail myfelf of this remark, I farther ob-
ferve, that we ought not to fay, that we fee the
moon greater in the horizon, than at a confiderable
elevation. This is abfoiutely falfe, for we then fee
her even fomewhat lefs. Eut to fpeak accurately,
we ought to fay that we judge and compute the
moon greater when me is in the horizon ; and this
is literally true with the unanimous confent of all
mankind. This is fufheient to reconcile the apparent
1 contradiction
446 REFLECTIONS RESPECTING THE
i
contradiction formerly fuggefted j for nothing pre-
vents our judging or computing the moon to be
greater when Ihe rifes or lets, though Ihe is feen
under a fmaller vifual angle.
IV. We are no longer, then, called upon to ex-
plain why we fee the moon greater in the horizon,
which is impoffible, for, in reality, Ihe then appears
fmaller, as may be demonftrated by meafuring the
vifual angle. The difficulty, therefore, is reduced to
this ; Wherefore do we judge or compute the moon
to be greater, when in thofe fituations ? or rather,
we muft endeavour to account for this whimfical.
computation. The thing is not furprizing in itfelf,
as we know a thoufand cafes in which we eftimate
objects to be very great, though we fee them under
very fmall angles.
V. We have only to fay, then, that when the
moon is riling or fetting, we fuppofe her to be at a
greater diftance, than when fhe has attained a certain
elevation. Whenever this computation is fettled,
whatever may be the caufe of it, the confequence is
neceifary, that we muft likewife conclude the moon
to be greater in proportion. For in every cafe, the
more diftant we eftimate any object to be, the greater
we prefume it is, and this in the fame proportion.
As foon as I imagine, by whatever illution, that a fly
pafiing clcfe before my eye is at the diftance of ioo
paces, I am obliged, almoft whether I will or no, to
fuppofe it as many times greater as ioo paces exceed
the real diftance of the fly from my eyes.
VI. We are now, therefore, reduced to a new
7 queftion :
moon's apparent magnitude. 447
queflion : Wherefore do we prefume that the moon
is at a greater diftance when me is feen in the hori-
zon ? and, Wherefore is this illufion fo univerfal as
not to admit of a fingle exception ? For the illufion
of imagining that the moon is then at a much greater
diftance is altogether unaccountable. It is undoubt-
edly true that the moon is, then, really a little more
diftant, as I demonftrated in my laft letter, but the
difference is fo trifling as to be imperceptible. Be-
fides, the fun, though 100 times more diftant than
the moon, does not appear fo, and the eye eftimates
even the fixed ftars as nearly at the fame diftance.
VII. Though, therefore, when the moon is in the
horizon, me is actually a little more diftant, this cir-
cumftance cannot affect, the prefent queftion ; and
this univerfal computation, which induces the whole
world to imagine the moon to be then at a much
greater diftance than me really is, muft be founded
on reafons entirely different, and capable of producing
univerfal illufion. For, as the computation is un-
queftionably erroneous, the reafons which determine
us to make it muft neceffarily be very ftriking.
VIII. Some philofophers have attempted to ex-
plain this phenomenon, by alleging, that it is occa-
fioned by the intervention of various objects between
us and the moon, fuch as cities, villages, forefts, and
mountains. This, fay they, is the reafon that fhe
then appears to be much farther off; whereas, when
fhe has attained a confiderable elevation, as.no other
body intervenes, fhe muft appear to be nearer. But
this explanation, however ingenious it may at firft
fight
44-8 APPEARANCE OF THE MOON
fight appear, is deftitute of folidity. On looking at
the moon in the horizon, through a fmall aperture
made in any body which mall conceal the interme-
diate objects, me neverthelefs ftill feems greater.
Befides, we do not always imagine that objects, be-
tween which and us many other bodies interpofe,
are more diftant. A great hall, for example, when
quite empty, ufually appears much larger than when
filled with company, notwithstanding the numerous
objeclis then interpofed between us and the walls of
the apartment.
24/^ rfpril, 1762.
LETTER CXII.
An Attempt toward the true Explanation of this Pheno*
menon : The Moon appears more dijlant when In the
Horizon, thani when at a great Elevation.
E are ftill, then, very far from the true folu-
tion of tins univerfai illufion, under which
all, without exception, are induced to imagine the
moon to be much greater when in the horizon, than
when conliderably elevated. I have already re-
marked, that this phenomenon is fo much the more
unaccountable, from it's being demonflrable that the
moon's apparent diameter is then even fomewhat
lefs : we ought not, therefore, to fay, that we then
fee the moon greater, but that we imagine her to
be fo.
Accordingly, I have very often obferved our judg-
ment
IN THE HORIZON. 449
ment of objects to differ very widely from vifion it-
felf. We do not hefitate, for example, to conclude,
that a liorfe 100 paces diilant is larger than a dog
one pace diftant, though the apparent magnitude of
the dog is unqueftionably greater, or, which amounts
to the fame thing, though the image of the dog,
painted on the bottom of the eye, be greater than
that of the horfc.. Our judgment, in this cafe, is
regulated by taking diftance into the account, and
laying it down that the horfe is much farther off
than the doo:, we conclude he is much larger.
It is very probable, therefore, that the fame cir-
cumftance may take place refpecting the moon's ap-
pearance, and induce us to reckon the moon greater,
when in the horizon, than at a considerable elevation.
In the cafe of the horfe, our computation of diftance
was founded in truth ; but here, as it is abfolutely
erroneous, the illufion muft be fingularly unaccount-
able, but muft, at the fame time, have a certain
foundation, as it's prevalence is univerfal, and can-
not, therefore, be imputed to caprice. Wherein
can it confifl ? This is to be the iubject of our pre-
fent enquiry.
I. Every one confiders the azure expanfe of hea-
ven as a flattened arch, the fummit of which is much
nearer to us than the under part, where it meets the
horizon. A perfon, accordingly, {landing on a plane
AB (plate X*flg. 7.) which extends as far as his
fight perceives the vault of heaven, commonly called
the firmament, under the figure AEFB, in which
Vol. II. G 2 the
450 APPEARANCE OF THE MOON
the diftances C A and G B are much greater than
from the zenith to C.
II. This idea is likewife, beyond all queftion, a
mere illufion ; there being, in reality, no fuch vault
furrounding and inclofing us on every fide. It is a
void of immenfe extent, as it reaches to the moft
diftant of the fixed ftars, an interval that far exceeds
all power of imagination. I ufe the word void to
diftinguifti it from grofs terreflrial bodies. Forr near
the earth, fpace is occupied by our atmofphere ; and
beyond, by that fluid, infinitely more fubtile, which
we call ether.
III. Though this vault, however, has no real ex-
iftence, it poffenes an undoubted reality in our ima-
gination ; and all mankind, the philofopher as well
as the clown, are fubject to the fame illufion. On
the furface of this arch we imagine the fun, the moon,
and all the liars to be difpofed, like fo many brilliant
ftuds affixed to it ; -and though we have a perfect
conviction of the contrary, we cannot help giving
into the illufion.
IV. This being laid down, when the moon is in
the horizon, imagination attaches her to the point A
or B of this fuppofed vault, and hence we conclude
her diftance to be as much greater as we confider the
line C A or C B to be greater than C Z ; but when,
as fhe afcends, and approaches the zenith, we ima-
gine fhe comes nearer, and if fhe reaches the very
zenith we think fhe is at the leaft poflible diftance.
V. The illufion, as to diftance, neceflarily involves
that
IN THE HORIZON. 45 1
that which refpedfcs magnitude. As the moon at A
appears much farther from C, than in the zenith,
we are, in a manner, forced to conclude, that the
moon is really fo much greater j and that in the fame
proportion that the diftance C A appears to exceed
the diftance C Z. All will not, perhaps, agree in de-
termining this proportion ; one will fay, the moon
appears to him twice as great, when in the horizon ;
another will fay three times, and the generality will
declare for the medium between two and three j but
every one will infallibly agree in afferting thr.t the
moon appears larger.
VI. It maybe neceffary, here, to prefent you with
the demonftration of this proportion. The compu-
tation of magnitude is neceffarily involved in the
computation of diftance. When the moon is near
the horizon, we fee her (plate X. Jig. S.J under a
certain angle, fay MCA, the fpectator being at C :
and, when me is at a very great elevation, let N C D
be the angle under which we fee her. It is evident
that thefe two angles MCA and N C D are nearly
equal to each other, the difference being impercep-
tible,
VII. But, in the fir ft cafe, as we eftimate the
moon's diftance to be much greater, or equal to the
line C A, with reference to the imaginary vault
above defcribed, it follows, that we compute the
moon's diameter to be equal to the line M A. But,
in the other cafe, the diftance of the moon C D ap-
pears much fmaller, and, confequently, as the angle
NCI) is equal to the angle MCA, the computed
G g 2 magnitu-
45^ AFFEARANCE OF THE HEAVENS
magnitude D N will be much finaller than the com-
puted magnitude A M.
VIII. To put this beyond a doubt, you have only
to cut off from the lines CM and CA, the parts Cd
and C n equal to the lines C D and C N ; and as in
the two triangles C d n and C D N, the angles at the
point C are equal, the triangles themfelves are like-
wife fo, and, confequently, the line DN will be
equal to the line d n ; but d n- is evidently fmaller
than A M, and that, as many times as the diftance
C d imd C D is lefs than C A. This is a clear de-
monftration of the reafon why we eflimate the moon
to be greater when in the horizon, than when near
the zenith. , ■
z^th April, 1762.
LETTER CXIII.
The Heavens appear under the Form of an Arch flattened
toward the Zenith,
YOU will tax me, no doubt, with pretending to
explain one illufion by another equally unac-
countable. It may be faid, that the imaginary vault
of heaven is altogether as inconceivable as the in-
creafed appearance of the moon and the other hea-
venly bodies, when in, or near, the horizon. The
objection is not without foundation, and therefore
■ lays me under the neceffity of attempting to explain
tlie true reafon, why the heavens appear in the form
of an arch flattened toward the fummit. The fol-
' lowing
TOWARD THE ZENITH. 453
lowing reflections may, perhaps, be received as an
acquittance of my engagement.
I. In order to account for this imaginary vault,
it will be alleged that it proceeds from the appear-
ance of the heavenly bodies, as feeming more re-
mote, when in the horizon, than when near to, or
in, the zenith. This is, undoubtedly, a formal petl-
tio principii) as logicians call it, or a begging of the
queition, which every one is entitled to reject as a
ground of reafoning. In truth, having faid above,
that the imaginary vault of heaven makes the moon,
in the horizon, appear farther off than when near
the zenith, it would be ridiculous to affirm, that
- the thing which leads us to imagine the exiftence of
fuch a vault is, that horizontal objects appear more
diftant than vertical.
II. It was not, however, ufelefs to fuggeft the
idea of this imaginary vault, though it may not
carry us a great way forward ; and after I {hall have
explained, wherefore the heavenly bodies appear
more remote when viewed near the horizon, you
will be enabled to comprehend, at the fame time,
the reafon of that two-fold univerfal illufion, namely,
the apparently increafed magnitude of the heavenly
bodies, when in the horizon, and the flattened arch
of heaven.
III. The whole, then, reverts to this, to explain
wherefore the heavenly bodies, when feen in the ho-
rizon, appear more remote than when at a conii-
derable elevation : I now affirm, it is becaufe thefe
objects appear lefs brilliant ; and this impofes on me
O g 3 th<3
454 APPEARANCE OF THE HEAVENS
the double talk of demonftrating, why thefe objects
difplay lefs brilliancy when in, or near, the horizon ;
and of explaining, how this circumftance neceffarily
involves the idea of a greater diftance. I flatter my-
felf I fhall be enabled to difcharge both of thefe to
your fatisfadtion.
IV. The phenomenon itfelf will not be called in
queftion. However greater the fun's luftre may be
at noon, which it is then impbffible to afcertain, you
know that in the morning and evening, when he is
riling or fetting, it is poffible to contemplate his
body, without any injury to the eye ; attid the fame
thing takes place with refpecl to the moon and all
the ftars, whofe brilliancy is greatly diminilhed in
the vicinity of the horizon. We, accordingly, do
not fee the fmaller ftars when at a fmall elevation
above the horizon, though they are fufficiently dif-
cernible at a certain height.
V. This being eftablilhed beyond a poflibility of
doubt, the caufe of this difference of illumination
remains to be inveftigated. It is abundantly evident
that we can trace it only in our atmofphere, or the
body of air which encompaffes our earth, in as far
as it is not perfectly tranfparent. For if it were, fo
that all the rays Ihould be tranfmitted through it,
without undergoing any diminution, there could be
no room to doubt, that the ftars mull always mine
with the fame luftre, in whatever region of the hea-
vens they might be difcovered.
VI. But the air, a fubftance much lefs fine and
fubtile than ether, whofe tranfparency is perfecl:, is
continually
TOWARD THE ZENITH. 455
continually loaded with heterogeneous particles,
riling into it above the earth, fuch as vapours and
exhalations, which deftroy it's tranfparency ; fo that
if a ray fhould fall in with fuch a particle, it would
be intercepted, and almoft extinguifhed by it. It is
accordingly evident, that the more the air is loaded
with fuch particles, which prevent the tranfmiflion
of light, the more rays muft be loft by the intercep-
tion ', and you know that a very thick mift deprives
the air of almoft all it's tranfparency, to fuch a de-
gree, that it is frequently impofllble to diftinguifh
objects at three paces diftance,
VII. Let the points marked, in plate X. fig. 9. re-
prefent fuch particles, fcattered through the air,
whofe number is greater or lefs, according as the air
is more or lefs tranfparent. It is evident, that many
of the rays, which pervade that fpace, muft be loft,
and that the lofs muft be greater, in proportion as
the fpace which they had to run through that air is
greater. We fee, then, that diftant objects become
invifible in a fog, while fuch as are very near the
eye, may be ftill perceptible, becaufe the rays of the
firft meet, in their progrefs, a greater number of
particles which obftruct their tranfmiflion.
VIII. We muft hence conclude, that the longer
the fpace is, through which the rays of the heavenly
bodies have to pafs through the atmofphere, in order
to reach our eyes, the more confiderable muft be
their lofs or diminution. Of this you can no longer
entertain any doubt, All that remains, then, is
fimply to demonftrate, that the rays of the ftars
G g 4 which
456 LIGHT OF HEAVENLY BODIES
which we fee in, or near, our horizon, have a longer
fpace of the atrnofphere to pervade, than when nearer
the zenith. When this is done, you will eafily com-
prehend, why the heavenly bodies appear much lefs
brilliant when near the horizon, than at the time of
riling and fetting. This fhall be the fubjecl of my
next letter.
17? May, 176a.
LETTER CXIV.
Reafon ajfgned for the Falntnefs of the Light of Hea-
venly Bqdies in the Horizon.
"W THAT I have juft advanced, namely, that the
\ ▼ rays of the heavenly bodies, when in the
horizon, have a larger portion of our atrnofphere to
pervade, may appear fomewhat pavadoxical, confider-
ing that the atrnofphere univerfally extends to the
fame height, fo that, at whatever point the ftar may
be, it's rays mult always penetrate through the whole
of that height, before it can reach our .eyes. The
following reflections, I flatter myfelf, will give you
complete fatisfaclion on the fubjecl.
I. It is, firft of all, neceffary to form a juft idea of
the atrnofphere which furrounds our globe. For
this purpofe, the interior circle A B C D (plate X.
fig. 10. J fhall reprefent the earth, and the exterior
dotted circle abed fhall mark the height of the at-
rnofphere. Let it be remarked that, univerfally, in
proportion as the air rifes above the furface of the
earth,
IN THE HORIZON. 456
earth, it becomes always more tranfparent and fub-
tile, fo that, at laft, it is imperceptibly loft in the
ether, which fills the whole expanfe of heaven.
II. The gr oiler air, that which is moft loaded with
the particles that intercept and extinguish, the rays of
light, is univerfally found in the lower regions, near
the furface of the earth. It becomes, therefore, more
fubtile as we afcend, and lefs obftru£tive of the light;
and, at the height of a German mile, has become fo
tranfparent, as to occafion no perceptible obftruction
whatever, of the light. The diftance, then, between
the interior circle and the exterior, may be fixed at a
German mile, nearly, whereas the femi-diameter of
the globe contains about 860 of fuch miles : fo that
the height of the atmofphere is a very fmall matter,
compared with the magnitude of the globe.
III. Let us now coniider, (plate X.flg. 11.) a fpec-
tator at A, on the furface of the earth ; and drawing
from the centre of the globe G, through A, the line
G Z, it will be directed toward the zenith of the fpec-
tator. The line A S, which is perpendicular, and
touches the. earth, will be horizontal to it. Confe-
quently, he will fee a ftar at Z in his zenith, or in
the fummit 'of the heavens ; but a ftar at S will ap-
pear to him in the horizon, at it's riling or fetting.
Each of thefe ftars may be considered as infinitely
diftant from the earth, though it wras impoflible to
reprefent this in the figure.
IV. Now you have only to caft your eye once
more on the figure, to be fatisfied that the rays pro-
ceeding from S have a much longer fpace to travel
through
4$& LIGHT OF HEAVENLY BODIES
through the atmofphere, than thofe from the ftar Zy
before they reach the fpectator at A. Thofe from the
liar Z liave only to pafs through the perpendicular
height of the atmofphere a A, which is not above a
German mile ; whereas thofe that come from the
ftar S have to travel the whole fpace h A, which is
evidently much longer ; and could the figure be re-
prefented more conformably to the fact, fo as to ex-
hibit the radius G A 860 times longer than the
height A a. v/e ihould find the diftance A h to exceed
40 fuch miles.
V. It is farther of importance to remark, that the
rays of the ftar Z have but a very fmall fpace to travel
through the lower region of the atmofphere, which
is moft loaded with vapour ; whereas the rays of the
ftar S have a much longer courfe to perform through
that region, and are obliged to crawl, if I may ufe
the exprefiion, along the furface of the earth. The
conclulion, then, is obvious. The rays of the ftar Z
undergo fcarcely any diminution of luftre, but thofe
of the ftar S muft be almoft extingaiifhed from fo
o
Ion sr a paiTa^e throug;h the proffer air.
VI. It is indifputably certain, then, that the ftars
which we fee in the horizon, muft appear with a
luftre extremely diminifhed ; and it will limply ac-
count to you for a well-known fa£t, that you can,
without any inconvenience, fix your eyes fteadily on
the rifin-g or fetting fun, whereas at noon, or at a
confiderable elevation, his luftre is infupportable.
This is the firft point I undertook to demonftrate ;
I proceed to the fecond, namely, to. prove that it is
the
IN THE HORIZON. 459
the diminution of light which forces us, almoft, to
imagine the heavenly bodies at a much greater dis-
tance, than when we fee them in all their luftre.
VII. The reafon muft be fought in terreftrial bo-
dies, with which we are every day converfant, and
reflecting whofe diftance we form a judgment. But
for the fame reafon that rays of light, in palling
through the air, undergo fome diminution of luftre,
it is evident, that the farther an object is removed
from us, the more of it's luftre it lofes, and the more
obfcure it becomes in proportion. Thus a very diftant
mountain appears quite dark ; but, on a nearer ap-
proach, we can eafily difcover trees on it, and other
minuter objects, which it was impoffible to diftin-
guifli at a very remote diftance.
VIII. This obfervation, fo general, and which never
mifleads us in contemplating terreftrial bodies, has
produced in us, from our childhood, this funda-
mental principle, from which we conclude objects to
be diftant in proportion as the rays of light which
they emit are weakened. It is in virtue of this prin-
ciple, therefore, that we conclude the moon to be
farther off at rifing and fetting, than at a coniiderable
elevation ; and for the fame reafon we conclude fhe
is fo much greater. You will, I flatter myfelf, admit
this reafoning to be folid ; and this embarrafling
phenomenon to be as clearly elucidated as the nature
of the fubject permits.
^.h May, 1762.
LETTER
460 „ ILLUSION RESPECTING THE
LETTER CXV.
II! iff on ref peeling the Dlftance of ObjeEls^ and the Dimi-
nution of Lujire.
*HE principle of our imagination, by which I
have endeavoured to explain the phenomenon
of the moon's greater apparent magnitude in the ho-
rizon than at a considerable elevation, is fo deeply
rooted in our nature as to become the fource of a
thoufand fimilar illuiions, fome of which I will take
the liberty to fuggeft.
We have been habituated from infancy, almoft in-
voluntarily, to imagine objects to be diftant in pro-
portion as their luftre is diminiihed : and, on the
other hand, very brilliant objects appear to be nearer
than they really are. This illufion can proceed only
from an ill-regulated imagination, which very fre-
quently mifleads us. It is nevertheless fo natural,
and fo univerfal, that no one is capable of guarding
again it it, though the error, in many cafes, is ex-
tremely palpable, as I have mewed in the.inftance of
the moon : but we are equally deceived in a variety
of other inftances. As I mail prefently make appear.
I. It is a well-known illufion, that the flame of a
conflagration, m the night, appears much nearer
than it really is. The reafon is obvious ; the fire
blazes in all it's luftre, and in conformity to a prin-
ciple pre-eftablifhed in the imagination, we always
conclude it to be nearer than it is in reality.
II. For
Vei.1T.
JP/*f<XL
DISTANCE OF OBJECTS. 461
II. For the fame rcafon, a great hall, the walls of
which are perfectly white, always appears fmaller.
White, you know, is the moft brilliant colour: hence
we conclude the walls of fuch an apartment to be too
near, and, confequently, the apparent magnitude is
thereby diminifhed.
III. But in an apartment hung with black, as is
the cuftom in mournings, we perceive the directly
oppoiite effect. The apartment now appears con-
fiderably more fpacious than it really is. Black is,
undeniably, the moft gloomy of colours, for it re-
flects fcarcely any light on the eye ; hence the walls"
of an apartment in deep mourning feem more di£
tant than they are, and confequently greater ; but
let the black hansrino's be removed, and the white
colour re-appear, and the apartment will feenl con-
tracted.
IV. No clafs of men avail themfelves more of this
natural and univerfal illufiori than painters. The
fame picture, you know, reprefents fome objects as
at a great diftance, and others as very near ; and
here the fkiil of the artift is moft confpicuous. It is
not a little furprizing, that though we know, to ab-
folute certainty, all the reprefentations of a picture to
be expreffed on the fame fur face, and, confequently,
at nearly the fame diftance from the eye, we mould
be, neverthelefs, under the power of illulion, and
imagine fome to be quite near, and others extremely
diftant. This illulion is commonly afcribed to a
dextrous management of light and made ; which,
undoubtedly, furnifh the painter with endiefs re-
fources.
462 DISTANCE OF OBJECTS.
fources. But you have only to look at a picture to
be fenfible, that the objects intended to be thrown to
a great diftance, are but faintly and even indiftinctly
expreffed. Thus, when the eye is directed to very-
remote objects, we eafily perceive, for example, that
they are men, but it is impoflible to diftinguifti the
parts, fuch as the eyes, the nofe, the mouth ; and it
is in conformity to this appearance, that the painter
reprefents objects. But thofe which he intends
ihould appear clofe to us, he difplays in all the
brightnefs of colouring, and is at pains clearly to ex-
prefs each minute particular. If they are perfons,
we can diftinguifti the fmalleft lineaments of the face,
the folds of the drapery, &c: this part of the re-
prefentation feems, I may fay, to rife out of the can-
vas, while other parts appear to link and retire.
V. On this illufion, therefore, the whole art of
painting entirely refts. Were we accuftomed to form
our judgment in ftrict conformity to truth, this art
would make no more impreflion on us than if we
were blind. To no purpofe would the painter call
forth all his powers of genius, and employ the hap-
pieft arrangement of colours, we fliould coldly affirm,
on that piece of canvas, there is a red fpot, here a
blue one ; there a black ftroke, here fome whitifh
lines : every thing is on the fame plane furface ; there
is no riling nor finking; therefore no real object can
be reprefented in this manner: the whole would, in
this cafe, be confidered as a fcrawling on paper, and
we fliould, perhaps, fatigue o.urfeives to no purpofe,
in attempting to decypher the meaning of all thefe
7 different
COLOUR OF THE HEAVENS. 463
different coloured fpots. Would not a man, in i'uch
aitate of perfection, be an object of much companion,
thus deprived of the pleafure refulting from the pro-
ductions of an art, at once fo amufing, and fo in-
itruclive ?
%tb May, 1762.
LETTER CXVI.
On the Azure Colour of the Heavens.
YOU are now enabled to comprehend the reafon
why the fun and moon appear much greater
when in the horizon, than at a confiderable eleva-
tion. It confifts in this, that we then unintentionally
compute thefe bodies to be at a greater diftance, a
computation founded on the very confiderable dimi-
nution which their luftre, in that pofition, undergoes,
from the longer paifage which the rays have to force,
through the lower region of the atmofphere, which
is the moft loaded with vapours and exhalations,
whereby the tranfparency is diminifhed. This is a
brief recapitulation of the reflections which I have
taken the liberty to fuggeit on this fubject.
This quality of the air, which diminimes tranfpa-
rency, might, at firft fight, be considered as a defect'
But on attending to confequences, we mall find it fo
far from being flich,that we ought, on the contrary,
to acknowledge in it the infinite wifdom and good-
nefs of the Creator. To this impurity of the air
we are indebted for that wonderful and raviihinsr
o
ipectacle
464 ON THE AZURE COLOU&
fpe.ctacle which the azure of the heavens prefents to
the eye ; for the opaque particles, which obftruct the
rays of light, are illuminated by them, and afterwards
re-tranfmit their own proper rays, produced in their
furface by a violent agitation, as is the cafe in all
opaque bodies. Now, it is the number of vibrations
communicated to them, which reprefents to us this
magnificent azure : a circumftance which well de-
ferves to be completely unfolded. .
I. I obferve, firft, that thefe particles are extremely
minute arid confiderably diftant from each other, be-
sides their being delicately, fine and almoft wholly
tranfparent. Hence it comes to pafs, that each, fe-
parately, is abfolutely imperceptible, fo that we can
be affected by them only when a very great number
tranfmit their rays at once to,the eye, and nearly in
the fame direction. The rays of feveral mufe, there-
fore, be collected, in order to excite a fenfation.
II. Hence it clearly follows, that fuch of thefe par-
ticles as, are near to us efcape our fenfes, for they
muft be confidered as points difperfed through the
mafs of air.
But fuch as are very diftant from the eye, as {plate
XL Jig. 1.) the points ab c collect in the eye, almoft
according to the fame direction, their feveral rays,
which, thus, become fufficiently ftrong to affect the
light, efpecially when it is confidered that fimilar
particles more remote, efg h, as well as others more
near, concur in producing this effect.
III. The azure colour which we fee in the heavens,
when ferene^ is nothing elfe, then, but the rcfult of
all
OF THE HEAVENS. 465
all thefe particles difperfed through the atmofphere,
efpecially of fuch as are very remote : it may be af-
firmed, therefore, that they are in their nature blue,
but a blue extremely clear, which becomes not fuf-
ficiently deep and perceptible, except when they are
in a very great number, and unite their rays accord-
ing to the fame direction.
IV. Art has the power of producing a fimilar effect.
If, on diffolving a fmall quantity of indigo, in a great
quantity of water, you let that water fall drop by
drop, you will not perceive in the feparate drops the
flighted appearance of colour ; and on pouring fome
of it into a fmall goblet, you will perceive- only a
faint bluifh colour. But if you fill a large veffel with
the fame water, and view it at a diftance, you will
perceive a very deep blue. The fame experiment
may be made with other colours. Burgundy wine,
in very fmall quantities, appears only to be faintly
reddifh, but in a large flafk completely filled, the
wine appears of a deep red.
V. Water, in a large and deep veffel, prefents fome-
thing like colour, but, in a fmall quantity, is alto-
gether clear and limpid. This colour is, commonly,
more or lefs of a greenifh caft, which may warrant us
in faying, that the minute particles of water are like-
wife fo, but of a colour fo delicately fine that a great
mafs of it mult be collected, before the colour can be
perceptible, becaufe the rays of a multitude of par-
ticles then concur toward producing this effect.
VI. As it appears probable, from this obfervation,
that the minute particles of water are greentfh, it
Vol. II. Ii h misrht
466 COLOUR OF THE HEAVENS.
might be maintained, that the reafon why the fea, or
the water of a lake or pool, appears green, is the very
fame that gives the heavens the appearance of azure.
For it is more probable, that all the particles of the
air ihould have a faintly bluifli caft, but fo very faint,
as to be imperceptible till prefented in a prodigious
mafs, fuch as the whole extent of the atmofphere ;
than that this colour is to be afcribed to vapours
floating in the air, but which do not appertain to it.
VII. In fact, the purer the air is, and the more
purged from exhalation, the brighter is the luftre of
heaven's azure ; which is a fufficient proof, that we
muft look for the reafon of it, in the nature of the
proper -particles of the air. Extraneous fubftances
mingling with it, fuch as exhalations, become, on
the contrary, injurious to that beautiful azure, and
ferve to diminifh it's luftre. When the air is over-
loaded with fuch vapours, they produce fogs near
the furface, and entirely conceal from us the azure
appearance ; when they are more elevated, as is fre^.
quently the cafe, they form clouds, which frequently
cover the whole face of the fky, and prefent a very
different colour from that of this azure of the pure
air. This, then, is a new quality of air, different
from thofe formerly explained, fubtility, fluidity and
elafticity ; namely, the minute particles of air, are in
their nature bluifh.
iltb$tayt ij6z.
LETTER.
OF TRANSPARENT AIR. 467
LETTER CXVII. -
What the Appearance would be, were the Air perfectly
tranfparent.
INDEPENDENT of the beautiful fpeftacle of the
azure heavens, procured for us by this colour of
the .circumambient air, we mould be miferable in the
extreme, were it perfectly tranfparent, and diverted
of thofe bluifh particles ; and we have here a new
reafon for adoring the infinite wifdom and goodnefs
of the Creator.
That you may have full conviction of the truth of
my affertion, let us fuppofe the air to be quite tranf-
parent, and fimilar to the ether, which, we know,
tranfmits all the rays of the liars, without intercept-
ing fo" much as one, and contains no particles them-
lelves illuminated by rays, for fuch a particle could
not be fo, without intercepting fome of the rays
which fell upon it. If the air were in this ftate, the
rays of the fun would pafs freely through it, without
the re-tranfmiffion of any light to the eye : we mould
receive, then, thofe rays only which came to us im-
mediately from the fun. The whole heavens, except
the fpot occupied by the fun, would appear, there-
fore, completely dark; and, infliead of this brilliant
blue, we mould difcover nothing, on looking up-
ward, but the deepeil black and the moft profound
night.
Plate XL fig, 2, reprefents the fun ; and the point
H h 2 O is
468 OF f RAIsfSPAREftT AIR.-
O is the eye of a fpectator, which would receive,
from above, no other rays but thofe of the fun, fey
that all illumination would be limited to the fpace of
the fhiall angle EOF. On directing the eye toward
any other quarter of the heavens, fay toward M, not
a fmgle ray would be emitted from it; and the ap~
pearance would be the fame as if we looked into total
darknefs; now, every place which tranfmits no ray
of light is black. But, here, the liars muft be ex-
cepted, which are fpread over the whole face of the
heavens; for on directing the eye toward M, nothing
need prevent the rays of the ftars which may be in
that quarter, from entering into it ; nay, they would
have even ftill more force, as they could fuffer no
diminution of luftre from the atmofphere, fuch as I
am now fuppofing it. All the ftars, therefore, would
be vifible at noon-day, as in the darkeft night ; but,
it muft be conlidered, that this whole day would be
reduced to the fpace of the little angle EOF; all the
reft of the heavens would be black as night.
At the fame time, ftars near the fun would be in-
vifible, and we mould not be able to fee, for example,
the ftar N, for on looking to it, the eye would like-
wife receive the rays of the fun, with which it muft
be ftruck fo forcibly, that the feeble light of the ftar
could not excite any fenfation. i fay nothing of the
impoffibility of keeping the eye open, in attempting
to look toward N. This is too obvious not to be
underftood.
But on oppofmg to the fun an opaque body, which
(ball intercept Jiis rays, you could not fail to fee the
2 ftar
Of TRANSPARENT AIR, 469
ilar N, however near it might be to the fun. It is
jeafy to comprehend in what a difmal Hate we iliould
then be. This proximity of lultre infupportable>
and darknefs the moil profound, mult deftroy the
-organs of virion, and quickly reduce us to total blind-
nefs. Of this fome judgment may be formed from
.the inconvenience we feel on palling fuddenly from
darknefs into light.
Now, this dreadful inconvenience is completely
remedied by the nature of the air, from it's contain-
ing particles opaque to a very fmall degree, and fuf-
ceptible of illumination. Accordingly, the moment
the fun is above the horizon, nay fomewhat earlier,
the whole atmofphere becomes illuminated with his
. rays, and we are prefented with that beautiful azure
which I have defcribed, fo that our eyes, whichever
way directed, receive a great quantity of rays, ge-
nerated in the fame particles. Thus, on looking to-
ward M, (fee the fame figure as before) we perceive a
great degree of light, produced by this brilliant azure
of the heavens.
This very illumination of the atmofphere prevents
our feeing the liars by day : the reafon of this is ob-
vious. It far exceeds that of the liars, and. the greater
light always makes the letter to difappear ; and the
nerves of the retina, at the bottom of the .eye, bemg
already flruck by a very ftrong light, are no longer
fenfible to the impreflion made by the feebler light of
the liars.
You will pleafe to recollect that the light of the
full moon is upward of 300,000 times more faint
H h 3 thin
47© OF TRANSPARENT AIR.
than that of the fun ; and this will convince you,
that the light proceeding from the ftars, is a mere
nothing in comparifon with the light of the fun. But
the illumination of the heavens, in the day-time,
even though the fun {hould be over-clouded, is fo
great, as many thoufand times to exceed the light of
the full moon.
You rnuft have frequently perceived that, in the
night, when the moon is full, the ftars appear much
lefs brilliant, and that thofe only of fuperior magni-
tude are vifible, efpecially in the moon's vicinity ; a
fufficient proof, that the ftronger light always ab-
forbs the feebler.
It is, then, an unfpeakable benefit, that our atmo-
fphere begins to be illuminated by the fun, even be-
fore he rifes, as we are thereby prepared to bear the
vivacity of his rays, which would otherwife be in-
fupportable, that is, if the transition from night to
day were inflantaneous. The feafon during which
the atmofphere is gradually illuminated before fun-
rifing, and continues to be illuminated after he fets,
is denominated twilight. This fubject, from it's
importance, merits a particular explanation, which
I propofe to attempt in my next Letter : and thus,
one article in phyfics naturally runs into another.
l$th May, l,6z.
, LETTER
REFRACTION OF LIGHT. 47 I
LETTER CXVIII.
Refraclion of Rays of Light in the Atmofphere, and it's
Effecls.- Of the Twilight. Of the apparent rifing
and fetting of the Heavenly Bodies,
TN order to explain the caufe of the twilight, or
-*- that illumination of the heavens which precedes
the riling of the fun, and continues fome time after
he is fet, I muft refer you to what has been already
demonftrated refpecling the horizon and the atmo-
fphere.
Let the circle -A OBD {plate XL fig. 3.) represent
the earth, and the dotted circle a ob d the atmo-
fphere : let a point O be affumed on the furface of
the earth, through which draw the ftraight line
H O R I, touching the earth at O, and this line H I
will reprefent the horizon., which feparates that part
of the heavens which is vifible to us, from that which
is not. As foon as the fun has reached this line, he
appears in the horizon, both at riling and fetting,
and the whole atmofphere is then completely illu-
minated. But let us fuppofe the fun, before his rif-
ing, to be ftill under the horizontal line at S : from
which the ray S T R, grazing the earth at T, may
reach the point of the atmofphere, lituated in our
iiorizon ; the opaque particles which are there wiil
already be illuminated by that ray, and confequently
have become vifible. Accordingly, fome time be-
fore the riling of the fun, the atmofphere h 0 R over
H h 4 our
47^ REFRACTION OF RAYS OF LIGHT
our horizon begins to be illuminated at R, and in
proportion as the fun approaches the horizon, a
greater, part of it will be illuminated, till it becomes,
at length, completely luminous.
This reflection leads me forward to another phe-
nomenon equally intereffing, and very intimately
connected with it, namely, that the atinofphere dif-
covers to us the body of the fun and of the other
ftars, fome time before they get above the horizon,
and fome time after they have fallen below it, by
means of the refraction which rays of light undergo
on palling from the pure ether into the grolfer air,
which confiitutes our atmofphere ; of this I proceed
to give you the demonftration.
I. Rays of light do not continue to proceed for-
ward in a ftraight line any longer than they move
through a tranfparent medium of the fame nature.
As foon as they pafs from one medium to another,
they are diverted from their rectilinear direction,
their path is as it were broken off"; and this is what
we call refraction, which I formerly explained at con-
fiderable length, and demonftrated that rays, on
palling from air into giafs, and reciprocally, are thus
broken or refracted:
II. Now air being a different medium from ether.
when a ray of light panes from ether into air, it,
mult, of neceility, undergo fome refraction.
Thus, the arch of the circle A M B (plale XL
jig. 4.) terminating our upper atmofphere^ if a ray
of light M S,' 'from the ether, falls upon it at M, it
will hut proceed ftraight forward in the fame direc-
- tion
IN THE ATMOSPHERE. 473
tion M N, but will affume, on entering into the air,
the direction M R, fomewhat different from M N,
and the angle N M R is denominated the angle of
refraction, or, fimply, the refraction.
III. I have already remarked, that the refraction
is greater in proportion as the ray S M falls more
obliquely on the furface of the atmofphere j or as the
angle BMS is fmaller or more acute. For if the ray
SM falls perpendicularly on the furface of the atmo-
fphere, that is, if the angle B M S is a right angle,
no refraction will take place, but the ray will purfue
it's progrefs in the fame ftraight line. This rule is
univerfally applicable to every kind of refraction,
whatever may be the nature of the two media,
through which the rays travel.
IV. Let the arch of the circle A O B (plate XL
Jig, 5.) reprefent the furfaGe of the earth, and the
arch E M F terminate the atmofphere. If you draw
at O the line' O M V, touching the furface of the
earth at O, it will be horizontal. And if the fun
is ftill under the horizon at S, fo as to be ftill invi-
lible (for no one of his rays can yet reach us in a
ftraight line) the ray S M, being continued in a
ftraight line, would pafs over us to N ; but as it falls
on the atmofphere at M, and in a very oblique di-
rection, the angle FMS being very acute, it will
thence undergo a very considerable refraction ;
inftead of proceeding forward to N, would ai
the direction M O, fo that the fun would be act
viable to a perfon at O, though ftill confiderabl
474 REFRACTION OF LIGHT."
low the horizon at S, or, which is the fame thing,
below the horizontal line O M V.
V. However, as the ray MO, which meets the eye,
is horizontal, we affign that direction to the fun him-
felf, and imagine him to be actually at V, that is, in
the Jiorizon, though he is frill below it. And reci-
procally, as often as we fee the fun, or any other ftar,
in the horizon, we are anured they are ftill below it,
according to the angle S M V, which aftronomers
have obferved to be about half a degree, or, more
exactly, 32 minutes.
VI. In the morning, then, we fee the fun before
he has reached our horizon, that is, while he is yet
an angle of 32 minutes below it ; and in the even-
ing a confiderable time after he is really fet, as we
fee him till he has defcended an angle of 32 minutes.
We call that the true riling and fetting of the fun,
when he is actually in the horizon ; and the com-
mencement of his appearance in the morning, and
difappearing at night, we denominate the apparent;
rifing and fetting.
VII. This refraction of the atmofphere, which ren- '
ders the apparent rifing and fetting of the fun both
earlier and later than the real, procures for us the
benefit of a much longer day than we fhould enjoy,
did not the atmofphere produce this effect. Such is
the explanation of a very important phenomenon in
nature-
iSfb May, 176s.
LETTER
■ f LEVATION OF THE STARS. 4J $
LETTER CXIX.
The Stars appear at a greater Elevation than they are.
Table of Refraclions.
OU have now, no doubt, a clear idea of this
lingular effect of our atmofphere, by which the
fun and the other heavenly bodies are rendered vi-
iible in the horizon, though conliderably below it,
whereas they would be invifible but for the refrac-
tion. For the fame reafon, the fun, and all the hea-
venly bodies, always appear at a greater elevation
above the horizon than they really gre. It is necef-
fary, therefore, carefully to diftinguifti the apparent
elevation of a ftar, from what it would be were there
no atmofphere. I fhall endeavour to fet this in the
cleareft light poflible.
I. Let the arch AOB (plate XL fig. 6.) be part
of the furface of the earth, and O the fpot where
we are, through which draw the ftraight line HOR,
touching the furface, and this line HOR will repre-
fent the true horizon. From O let there be drawn
perpendicularly the ftraight line O Z, which is the
fame thing as fufpending a given weight by a cord.
This line is faid to be vertical, and the point Z of the
heavens, in which it terminates, is called the zenith.
This line O Z, then, is perpendicular to the hori-
zontal H O R, fo that one being known, the other
muft be known likewife.
II. This being laid down, let {plate XI. fig. 7.)
ther.;
47$ . ELEVATION OF THE STARS.
there be a flar at S : were there no atmofphere, the
ray SMO would proceed in a ftraight line to the
€ye at O, and we fhpuld fee it in the fame direction
OMS, where it would actually be, that is, wefhould
fee it in it's true place. Let us, then, meafure the
angle SOR, formed by the ray S O with the horif
2011 OR, and this angle is named the height of the
ftar, or it's elevation above the horizon. We mea-
fure alfo the angle SOZ, formed by the ray S O
with the vertical line O Z terminating in the zenith :
and as the angle Z O R is a rieht angle, or 00 de-
grees, we have only to fubtract the angle SOZ from
90 degrees, to have the angje SO R, which gives
the true elevation of the ftar.
III. But let us now attend to the atmofphere,
which I mppofe terminated by the arch HDNMR;
and, I remark, firft, that the preceding ray S M of
the flar S, on entering into M in the atmofphere,
does not proceed direftly forward to the eye at O,
but, from the refraction, will afliime another direc-
tion as M P, and consequently will not meet the eye
at O : fo that If this liar fent down to the earth only
that ray S M, to a perfon at O it would be abfo-
lutely invifible. But it muft be confidered, that
every luminous point emits it's rays in all directions,
and that all fpace is filled with them.
IV. There will be, then, among others, fome ray,
as S N, which is broken or refracted, on entering
the atmofphere at N : fo that it's continuation N O
iliall pafs precifely to an eye at O. The refracted
ray N O is not, therefore, in a ftraight line With the
ray
KMiVATION OF TII'K STARS. 477
fay S M ; and if N O be produced forward to s, the
continuation N s will form an angle with the ray NS,
name)/, the angle S N s, which is what we call the
refraction, and which is greater in proportion as the
angle SNR, under which the ray S N enters into
the atmofphere, is more acute, as was demonftrated
in the preceding Letter.
V. It is the ray N O, confequently, which paints
in the eye the image of the ftar S, and which renders
it vifible : and as this ray comes in the direction NO,
as if the ftar were in it, we imagine the ftar likewife
to be lituated in the direction NO, or in that line
continued, fomewhere at s. This point s being dif-
ferent from the real place of the ftar S, we call s the
apparent place of the ftar, which muft be earefully
diftinguifhed from it's place S, where the ftar would
be feen, were there no atmofphere.
VI. Since, then, the ftar is feen by the ray NO,
the angle NOR, which this ray N O makes with
the horizon, is the apparent altitude of the ftar ; and
when, by a proper inftrument, we meafure the angle
NOR, we are laid to have found the apparent alti-
tude of the ftar ; the real altitude being, as we have
{hewed, the angle R O S.
VII. Hence it is evident, that the apparent alti-
tude RON5 is greater than the real altitude ROM,
fo that the ftars appear to us at a greater elevation
above the horizon than they really are, for the fame
reafon they appear already in the horizon while they
are ftill below it. Now the excefs of the apparent
altitude above the true, is the angle MON, which
differs
•4?8 ' ELEVATION OF THE STARS.
differs not from the S N s, and which we call the
refraction. For, though the angle S N s, as being
the external angle to the triangle S N O, is equal to
the two internal and oppofite angles taken together,
namely, SON and N S O, we may confider, on ac-
count of the immenfe diftance of the ftars, the lines
O S and N S as parallel, and, confequently, the angle
O S N vanishes ; fo that the angle S O N is nearly
equal to the angle of refraction S N s.
VIII. Having found, then, the apparent altitude
of a ftar, you muft fubtract from it the refraction, in
order to have the real altitude, which there is no
other method of difcovering. For this purpofe,
aftronomers have been at much pains to afcertain the
refraction to be fubtracted from each apparent alti-
tude, that is, to determine how much muft be abated
in order to reduce the apparent to the real altitude.
IX. From a long feries of obfervations, they have
been, at length, enabled to conftruct a table, called
the table of refraction, in which is marked for every
apparent altitude, the refraction, or angle to be fub-
tracted. Thus, when the apparent altitude is no-
thing, that is, when the ftar appears in the horizon,
the refraction is 32' minutes, the ftar is, accordingly,
an angle of actually 32 minutes below the horizon.
But if the ftar has acquired any degree of elevation,
be it ever fo inconfiderable, the refraction becomes
much lefs. At the altitude of 15 degrees it is no
more than four minutes ; at the altitude of 40 de-
grees it is only one minute ; and as the altitude en-
creafes, the refraction always becomes lefs, till, at
length
~Vo4.IT.
TUuir
k /j---~s^R
■F&3
.
ELEVATION OF THE STARS, 479
length, it entirely difappears, at the altitude of 90
degrees.
X. This is the cafe when a ilar is feen in the very-
zenith ; for it's elevation is then 90 degrees, and the
real and apparent altitude is the fame : and we arc
fully allured that a (tar feen in the zenith is actually
there, and that the refraction of the atmofphere does
not change it's place, as at every other degree of
altitude-
THE END,
GLOSSARY
O F
FOREIGN AND SCIENTIFIC TERMS.
»e>«55«®<!
A.
A BERRATION, In Aftronomy a flight deviation of a Star
■*■ *" from the ftated courfe. Latin.
Absorption, the aft of fucking or fwallowing up. Latin.
Abstraction, in Philofophy, that operation of the mind, which
purfues a general idea, without attending to the particulars
of which it is made up. Thus, Man, Tree, are abjira&l
ideas, and may be purfued, without defcending to any one
individual perfon or plant, included in the general term.
Accordingly, all qualities, fuch as whltenefs, cruelty, gene-
rojity, are abjlraSt ideas. Latin.
Accord, in Mufic, the fame with concord, the relation of two
founds which are always agreeable to the ear, whether
emitted at once or in fucceflion. Latin.
AcHROMATic-Glafles, in Optics, are a recent improvement of the
Telefcope, by which the inconveniency arifing from the
confufed tranfmiffion of different coloured rays is pre-
vented. The word is of Greek extraction, and fignifies
colourlefs.
Aeriform, Latin, having the form or confiftency of Air.
Aerostation, the art of afcending into the Atmofphere by means
of a Balloon filled with inflammable Air. Latin.
Vol. II. I i Affirmative,
482 GLOSSARY OF FOREIGN
AFFiRMATivE-propofition, in Logic, a propofition which aflerts
or affirms ; as Man is mortal. Latin.
Air-pump, a machine for making experiments on air, chiefly by
exhaufting clofe veflels of that fluid.
Algebra, an Arabic word; it is the Science of univerfal Arith-
metic ; the general procefs of which is, by comparing fup-
pofed and unknown numbers or quantities, with fuch as
are known, to reduce fuppofition into certainty.
Alkali, an Egyptian word } in Chemiftry, any fubftance which,
when blended with an acid, excites fermentation.
Altitude, in Aftronorhy* the height of a Star above the Hori-
zon. Latin.
Amalgamate, to incorporate mercury, or quickfilver, with
other metals ; fometimes ufed to denote, in general, the
mixture and confolidation of feveral fubftances, fo as to
make them appear one. Greek.
Analagous, having refemblance or agreement. Greek.
Analysis, refolution into firft principles, whether in grammar,
logic, mathematics, or chemiftry. To give an inftance,
in Grammar, which is perhaps the moft familiar to a
young perfon's mind, an analyjis of this fentence ; In the
beginning God created the Heavens and the Earth, is to indi-
cate the various parts of fpeech of which it is compoled,
and the grammatical rules according to which they are ar-
ranged. The child may innocently amufe himfelf with
the idea of a Chemical analr/Jis, by a fcientific procefs ap-
plied to a bowl of the vulgar liquor called punch. To
analyze it, is to afcertain, by feparation, the proportion
of fugar, lemon-juice, fpirit> and water, of which it is
compofed. Greek.
Anathema, and it's compounds ; fomething fet apart to a facred
ufe ; generally underftood in an ungracious fenfe ; devoted
to deftrudtion, accurfed. Greek.
Ak atomy, the fcience of the ftru6ture of the body, and the art
of differing and reafoning upon it. Greek.
Angle,
AND SCIENTIFIC TERMS. 483
Angle, the meeting of two lines in a point, but fo as not to form
of both one ftraight line. Latin.
Antecedent, in Logic, the former of two propositions, in a
fpecies of reafoning, which, without the intervention of
any middle propofition, leads directly to a fair conclufion ;
and this conclufion is termed the Confequent. Thus J re-
jleft ; therefore I exiji. I refleSt is the Antecedent, therefore
I exlfi is the Confequent. Latin.
Antipodes, the Inhabitants of the Globe diametrically oppofite
to us, and whofe feet prefent exactly to our feet. Greek.
Aperture, opening. Latin.
Approximation, a coming nearer to. In Aftronomy, the gra-
dual approach of two ftars toward each other : in Arith-
metic, a nearer approach to a number or root fought, with-
out the poflibility of arriving at it exactly. Latin.
Aqueduct, what conveys, or conducts water ; a pipe, a canal.
Latin.
Aqueous, watery, confifting of water. Latin.
Arithmetic, the fcience of numbers. Greek.
Astronomy, the fcience of the heavenly bodies. Greek.
Astrology, the pretended fcience of predi&ing future events by
means of the ftars. Greek.
Atmosphere, the body of air which furrounds the globe on all
fides. Greek.
Axis, in Geography, an imaginary ftraight line paffing through
the centre of the Earth from pole to pole, round which
the Globe revolves once every twenty-four hours. Latin.
B.
Barometer, an inftrument of glafs filled with quickfilver, which
indicates the prefTure of the air, and which is in general
ufe, as- an index of the weather. The word is Greek, and
fignifies weight-meafurer.
1 1 s Bisect,
484 GLOSSARY OF FOREIGN
Bisect, to cut into two equal parts. Latin.
Bituminous, like to, or confiding of bitumen, a fat, clammy,,
eafily inflammable juice, dug out of the earth, or fcummed
off lakes. Amber, pit-coal, and fulphur, are hard bitu-
mens, Latin.
Bomb, a hollow caft-iron globe, to be thrown from a fpecies of
great gun called " mortar" and intended to buril by the
force of gun-powder, at the moment of falling, and to
fcatter deflru&ion all around. It is in this Work inno-
cently employed to explain the path of all bodies forcibly
thrown through the air, and the effect, of gravity in bring-
ing all heavy moving bodies down to the ground. Latin.
Botany, the fcience of Plants ; or that part of natural and me-
dicinal hiftory which has the vegetable world for it's ob-
ject.. Greek.
C.
Camera Obsctjra, an apartment darkened, all but a fmall cir-
cular opening, to which a double-convex glafs is fitted,
and by which external objefts are reprefented in their na-
tural colours, motions, and proportions, on a white table
within the apartment. Latin.
Cataract, a body of water precipitated from a great height.
Greek.
Gatoptricks, that branch of the fcience of virion which relates
to reflected light. All bodies which you do not fee
through^ but which from their polilh and brightnefs throv>
beck the light, belong to catoptrich, fuch as mirrors of every
kind. The word is Greek, and fignifies backward vijion.
Cavity, a hollow. Latin.
Causa-sufficiens, J'ujicient or fatisfying cavfe or reafont a jargon
employed by certain Metaphyficians of the laft age, who
attempted to check all rational, experimental enquiry, by
calling continually for the caufa fujjicien$t the adequate caufe
of
AND SCIENTIFIC TERMS. ^85
of every faft that occurred, and of every obfervation that
was made ; while they were bewildering themfelves, and
attempting to bewilder mankind, in a philofophic maze,
ufclefs, reafonlefs, and therefore unfatisfaftory.
Centre, a point within a circle or fphere, equally diftant from
every point of the furface or circumference. Latin.
Chart, a delineation on paper of part of the land or of the fea,
or both. Latin.
Chemistry, or Chymistry, a word of uncertain derivation ;
the fciencc of feparating compound folid bodies, or of
compounding fimple bodies into one mafs, by the force of
fire.
Chimera, a vain and wild imagination, Latin.
CHORAL-mufic, a facred band compofed of voices and inftru-
ments. Latin.
Chromatic ; in Opticks, relating to colour ; in Mufic, to a cer-
tain feries of founds. Greek.
Circle, a round figure, having this eflential property, that every
point of it's furrounding line, called the circumference,
fhall be equally diftant from it's middle point, called the
centre. Latin.
Circumambient, encompalfing round and round : applied par-
ticularly to air and water. Latin.
Circumference, the furrounding line of a circle, every point of
which mull have an equal diftance from it's middle point
or centre. Latin.
Cohesion, clinging or nicking together. Latin.
Collision, the claming of one folid body againft another. Latin.
Comet, a ftar with a fiery train, like flowing hair, averted from
the fun ; of uncertain appearance and re-appearance, but
undoubtedly forming part of our folar fyitem. Greek.
Complex, made up of various qualities or ingredients. A beau-
tiful, wife and good woman, is a complex idea, containing
three diftinft ideas, beauty, wifdom, goodnefs ; you might
I i 3 render
4&6 .' GLOSSARY OF FOREIGN
render it ftill more complex by the addition of high-born,
rich, religious but I mult not make my idea too
complex.
Compression, the a<St of reducing to a fmaller fpace by preflure.
Concave, the hollowed furface of a globular body. Latin.
Concussion, mutual fhock, by violent meeting of two folid
bodies. Latin.
Condensation, the acl of contra&ing air into a fmaller fpace,
and thereby increafing it's elaftic force, that is, it's power
of burfting out. Latin.
Congelation, the reduction of a fluid to a folid fubftance, as
water to ice by cold. Latin.
Concentric Circles, one within another, having a common
centre. Latin.
Conical, having the form of a cone, which is a figure produced
by turning round a right-angled triangle about it's perpen-
dicular fide; a common candle extinguifher conveys the
idea of it. Greek.
Consequent. Take the trouble to look to the word Antecedent.
They are what is called correlative, in other words the one
cannot be underftood but by referring to the other.
Consonance? in Mufic, the agreement of two founds emitted at
the fame time. Latin.
Constituent, contributing to make up or compofe. Thus, the
conftituent parts of gun-powder are faltpetre, fujphur,
and charcoal. Latin. '
Continuity, uninterrupted connection ; the'unviolated union of
the parts of an animal body. Latin.
Contexture, an interweaving. Latin.
Contour, the extreme bounding line of any object.. Children
delineate the contours of each other's faces by tracing, with
a pencil, the line defcribed on the wall, when the face is
placed between a light and the wall. It is a French
word.
Convergent,
AND SCIENTIFIC TERMS. 487
Convergent, gradually approaching to each other. Placed at
the extremity of an avenue of two rows of trees, planted
in Straight lines, equally diftant throughout, you perceive
them apparently approaching, and at length almoft meet-
ing ; they are apparently convergent.
Convex, the prominent or fwelling Surface of a globular body,
Latin.
Cornea, the white, horny membrane of the eye. Latin.
Corporeal, belonging to body. Latin.
Corpus Callosum, in Metaphyfics and Anatomy, the part of
the human brain where the foul is fuppofed to refide.
Latin, but of ludicrous derivation.
Corpuscle, a finall or minute body. Latin.
Couching, an operation in Surgery, by which a film obftrudling
fight is by a needle or lancet removed from the aqueous
humours of the eye ; the word is of French extraction.
The film removed is denominated cataracl.
Crucible, an earthen pot which can Stand fire, employed in
melting and refining metals. Low Latin.
Crystalline, the lucid, various-coloured humour of the eye,
which forms a beautiful circle, inclofed by the cornea, and
inclofing the pupil, or central fpojt of that precious organ.
Greek.
Cube, and it's compounds ; a figure Square and rectangular in all
it's dimensions and Situations. A common die conveys
the idea of it. A cubical room of twenty feet, is a room
twenty feet long, twenty feet broad, and twenty feet high,
and all in ftraight lines, and at right angles. Greek.
Curve, a bending line. Latin.
Cylinder, a figure formed by turning a parallelogram round one
of it's fides as an axis. The barrel of a hand-organ is a
cylinder. The word is derived from a Greek verb, which
Signifies to wheel round.
I i 4 Decompose.
488 GLOSSARY OF FOREIGN
D,
Decompose, to feparate things compounded : thus, in printing,
to cowpofe is to arrange the types in a frame, in the order
of words and fentences ; and to decompofe is to take the
frame to pieces. Latin.
Degree, in Geography, the three hundredth and fixtieth part of
the circumference of the globe : it contains about 69 Eng-
liih miles. French.
Density, thicknefs. Latin.
Dephlogistic, deprived of fiery inflammable qualities. Greek.
Detonation, the thunder-like noife produced by firing off' heavy
artillery. Latin.
Diagram, a figure delineated for the purpofe of mathematical
demonstration. Greek.
Diameter, a ftraight line drawn through the centre of a circle or
globe, from circumference to circumference. Greek.
DiAphonous body, that which eafily tranfmits the light, as glafs.
Greek.
Diaphragm, in optical inftruments, a circular piece of paffe-
board, or other non-tranfparent fubftance, applied to the
objecl-glafs, to exclude part of the rays of light. Greek.
Diatonic, an epithet given to the common mufic, as it proceeds
by tones, both afcending and defcending. Greek.
Dilate, to expand, to fpread over greater fpace. Latin.
Dimension, meafure. Latin. \
Dioptricks, that branch of the fcience of vifion which relates to
the tranfmiflion of the rays of light through tranfparent bo-
dies. Greek.
Dissonance, in mufic, founds that do not harrnonize, but are
harfh and difagreeable to the ear. Latin.
Distraction, tendency in different directions. Latin.
Divergent,
AND SCIENTIFIC TERMS. 489
Divergent, ftraight lines, gradually removing farther and farther
from each other. See Convergent. Latin.
Diving-bell, a machine of wood, glafs, or metal, in form of a
bell, for the purpofe of conducting down into the water,
with fafety, perfons employed in certain kinds of fifhery,
and in recovering goods loft by {hipwreck.
Divisibility, capability of being divided. Latin.
Double-concave, an optical glafs which has both furfaces hol-
lowed.
Double-convex, an optical glafs whieh has both furfaces raifed.
Ducat, a ducal coin of gold, current on the continent, value
about nine {hillings and fixpence.
Ductile, pliant, eafily drawn or fpread out. Latin.
E.
Effulgence, luflre, brightnefs. Latin.
Elasticity, a power in bodies of recovering their former fitua-
tion, as foon as the force is removed, which had changed
it. Thus, the extremities of a bow are brought nearer by
drawing the ftring, but when the ftring is relaxed, the
bow, by it's elajiicity, is reftored to it's natural ftate. It
is a property of air, as well as of folid bodies. Greek.
Electricity, the difpofition which certain bodies have of ac-
quiring, by rubbing, the quality of attracting other bodies,
and of emitting fparks of fire. It is derived from a Latin
word fignifying amber, which is one of the fubftances en-
dowed with the eleftncal virtue.
Elicite, to ftrike out by force. Thus by a fharp ftroke of the
fteel on flint, fire is elicited. Latin.
Elogium, or Eulogium, an oration in praife of one abfent or
dead. Greek.
Elucidation,
49° GLOSSARY OF FOREIGN
Elucidation, the aft of explaining or rendering clearer. Latin.
Emanation, an ifTuing or flowing from any fubftance as a
fouree. Latin.
Emersion, in Afironomy, the re-appearance of a liar, after
having been obfcured by it's approach to the Sun, or by
the intervention of another ftar intercepting the Sun's
light. Latin.
Emission, the aft of fending but, or giving vent. Latin.
Encyclopedia, the whole circle of fcience: an univerfal fcien-»
tiflc Dictionary, deftined to the inftruftion of the young
and ignorant. Greek.
Epicurean, belonging to the doftrine or philofophy of Epicurus ;
according to which man's duty and happinefs are made to
conuft in fenfual indulgence, it is accordingly become de-
fcriptive of refined luxury.
Equator, an imaginary great circle, equally diftant from both
Poles, furrounding the Globe from Eaft to Weft, and di-
viding it into the Northern and Southern Hemifphere.
On it are marked the degrees of Longitude, from i to
360. It is by way of diftinftion called the Line. Latin.
Equidistant, at equal diftances. Latin.
Equilibrium, a Latin word, fignifying exaftnefs of balance or
counter-poife. The Latin ablative with the prepofition is
adopted into our language, in equilibrio, to exprefs perfeft-
nefs of equality in oppofed weights.
Equinox. The equalization of day and night, which takes place
twice every year about the middle of the months of March
and of September, when the Sun, in his alternate progrefs
from North to South, and from South to North, pafies
directly over the Equator, which is like wife, for this
very reafon, frequently denominated the Equinoctial Line.
Latin.
Era, an important event or period of time, from which, as a he-
ginning, computation of time is made. Latin.
Erudition,
AND SCIENTIFIC TERMS. 491
Erudition, extenfive and profound learning. Latin.
Ether, the moft fubtile and pure of all fluids. Greek.
Evaporation, the ad of flying off' by the force of heat in fumes
or vapor, Latin.
Exhalation, a word of the fame import with the former ; evapo-
ration may be confidered as the caufe, and exhalation as the
effect. Latin.
Expansibility, capability of being fpread out, and of covering
a larger furface. Latin.
Experiment, a practical trial made to afcertain any natural fact.
Latin.
Extension, fpace over which matter is diffufed; fize, magnU
tude. Latin.
Extraneous, not belonging to. Latin.
F.
Fathom, a meafure of length containing fix feet. Saxon.
Fibre, a fmall thread ; in Anatomy, fibres are long, (lender,
whitifh filaments, varioufly interwoven, which form the
folid parts of an animal body. Latin.
Fifth, in Mufic, one of the harmonic intervals or concords, and
the third in refpect of harmony, or agreeablenefs to the
car: it is thus called becaufe it contains Jive terms, or
founds, between it's extremes. See Vol. I. Letter VII.
Filament, the fame with fibre. Latin.
Fluid, confiding of parts eafily compreffible and feparabie, as
melted metals, water, air. Latin.
Flcx, in Geography, the rifing of the tide. Latin.
Focus, in Optics, the little circle in which rays of light are col-
lected, either after pairing through a glafs, or on being
thrown back from it, and where they exert their greateft
power of burning. Latin.
FORMULE,
493 GLOSSARY OF FOREIGN
Formule, a fet or prefcribed ftandard : a fcheme for folving ma-
thematical and algebraical queflions. Latin.
Forte, in Mufic, forcibly, in oppofition to piano, foftly. Latin.
Fourth, in Mufic, one of the harmonic intervals, and the fourth
in refped of agreeablenefs to the ear. It confifts of two
founds blended, in the proportion of 4 to 3 ; that is, of
founds produced by chords, whofe lengths are in the pro-
portion of 4 to 3. See Vol. I. Letters VI. and VII.
Friction, the acl: of rubbing one folid body againfl another.
Latin.
Fusible, that may be eafily melted. Latin.
G.
Gamut, the fcale of mufical notes. Italian.
Genus, kind, general clafs containing feveral fpecies, which
again contains many individuals. Thus, Dog is the genus ;
Greyhound is the /pedes, and light-foot the individual. The
Latin plural genera is in ufe.
Geography, a defcription of the Globe. Greek.
Geometry, the fcience of quantity, magnitude or extenfion ab-
ftractly confidered. Greek.
Glaucous, azure-coloured. Greek.
Globule, fmall globe ; little particles ©fa fpherical form. Latin.
Gradation, regular progrefs from one ftep to another. Latin.
Gravity, weight; in the fyftem of the Univerfe, that principle
in all bodies which prefies them down to, or attracts them
toward, their centre. Latin.
Groove, a channel cut out in a hard body with a tool, fitted to
another body which is defigned to move in it.
Harmohy,
AND SCIENTIFIC TERMS. 493
H.
Harmony, in Mufic, a combination of founds perfectly adapted
to each other, fo as to produce a pleafing effect on the ear.
Greek.
Hemisphere, one half of a, Globe. Greek.
Heterogeneous, made up of diffimilar or difcordant parts ; it is
the oppofite of homogeneous, which iignifies, made up of
things fimilar. Greek.
Horizon, the line which terminates the view. In Geography,
an imaginary circle encompaffing the Globe, and dividing
it into the upper and under Hemifpheres. To a perfon
placed at either of the Poles, the Equator would be the
real Horizon. The fenfible Horizon is the circle vifibly fur-
rounding us, where the fky and the earth meet. Greek.
Humidity, moifture. Latin.
Hydrography, a defcription of that part of our Globe which
confifts of water. ,
Hypothesis, a proposition or doctrine fuppofed to be true, but
not yet confirmed by irrefiftible argument or fatisfying ex-
periment. Greek.
I.
Idealist, a kind of Philofopher who denies the exiftence of
matter, and reduces every thing to idea or mental image.
Greek.
Illimitable, what admits of no bound. Latin.
Illumination, the acT: of difrurmg light. Latin.
Illusion, what deceives by a falfe appearance. Latin.
Immaterial, in Philofophy, not confirming of body or matter.
Latin.
Immersion, in Aftronomy, the difappearance of a ftar by a near
approach to the Sun, or the interception of it's light by
another ftar interpofing between the Sun and it. Latin.
Impenetrability,
494 GLOSSARY OF FOREIGN
Impenetrability, that property of all bodies, in virtue of which
no two can occupy the fame fpace, at the fame time.
Latin.
Impulsion, the agency of one body in motion upon another.
Latin.
Imputability, the quality of being charged upon, or afcribed
unto. Latin.
Incidence, the direction in which one body falls upon or ftrikes
another : and the angle formed by that line, and the plane
ftruck upon, is called the angle of incidence. Latin.
Index, the fore-finger, any inftrument that points out or indicates.
Latin.
Individual, one feparate, diftinct, undivided whole.
Inertia, that quality of bodies in virtue of which they are dif-
pofed to continue in a ftate of reft, when at reft, or of
motion, when in motion ; and which can be overcome
only by a power not in body itfelf. Latin.
Infinity, boundleflhefs, applied equally to fpace, number, and
duration: in infinitum without limit, without end. Latin.
Inflection, the act of bending or turning. Latin.
Inherent, naturally belonging to, and infeparable from. Latin.
Intellectual, relating to the underftanding, mental. Latin.
Intensity, the ftate of being ftretched, heightened, affected to a
very high degree. Latin.
Interception, the cutting off or obftruction of communication.
Latin.
Intersect, mutually to cut or divide. Latin.
Interstice, the fpace between one thing and another.
Inverse, having changed places, indirect, turned upfide down.
Latin.
Iris, the circle round the pupil of the eye. Latin.
Labyrinth,.
AND SCIENTIFIC TERMS. 495
L.
Labyrinth, maze, inextricable difficulty or perplexity. Latin.
Latitude, in Geography, meafurement of the Globe from the
Equator, Northward and Southward to the Poles, in de-
grees and minutes. The degree contains about 69 Englifh
miles, and a minute is the fixtieth part of a degree. The
higheft poffible degree of Latitude is at the Poles, each being
90 degrees from the Equator, Latin.
Lens, a round glafs, double-convex, for affifting vifion, or deriving
fire from the collecled rays of the Sun. Lenticular, having
the form of a lens.
Level, rifing or falling to the fame height." Saxon.
Literati, the learned; the plural of the Latin word Uteratus a
learned man.
Logic, the art of right reafoning, for the purpofe of invefti gating,
and communicating ufeful truth. Greek.
Longitude, in Geography, meafurement of the Globe in degrees
and minutes, round and round, from Eaft to Weft. Latin.
Lunar-tide, the flowing and ebbing of the tide relatively to the
Moon. Latin.
Lymphatic, vefTels, flender, tranfparent tubes through which
lymph, or a- clear colourlefs fluid is conveyed.
M,
Magnet, and it's compounds, a ftone which attracts iron and
fteel ; and gives a northerly direction to the needle of the
Mariner's Compafs. Art has been enabled, by means of
bars of fteel, fuccefsfully to imitate the natural magnet or
loadftone. Latin.
Magnitude, greatnefs, bulk, extenfior* Latin.
Manichean,
496 GLOSSARY OF FOREIGN
Manichean, one of a feci who maintained the exiftence of a fu«
preme evil fpirit.
Major, in Logic, the firft propofition of a fyllogifm, containing
fome general affertion or denial ; as, all men are mortal ; no
man is perfe&l. Latin.
Materialist, one who denies the exiftence of fpi ritual fubftances.
Latin.
Mathematics, the Science which has for its object every thing
capable of being meafured or numbered. Greek.
Mean, or Medium^ in Phyfics, fomewhat intervening between
one fubftance and another: in Logic, an intermediate
propofition employed to lead to a fair and juft conclufion.
Latin.
Mechanics, the Geometry of motion; the Science Ofconftruft-
ing moving machinery. Greek.
Membrane, a web of various fibres interwoven, for wrapping up
certain parts of vegetable and animal bodies. Latin.
MENiscus-lens, in Optics, a glafs which is convex on one furface,
and concave on the other.
Mephites, poifonous, ill-fcented vapor. Latin.
Mercury, the chemical name of the fluid commonly called quick-
Jiher. Latin.
Meridian, in Geography, a great circle encompafling the Globe
in the direction of South and North, and dividing it into
the eaftern and weftern Hemifpheres. . The degrees of La-
titude, from the Equator to both Poles, are marked on this
circle. Every fpot of the Globe comes to it's meridian once^
in every twenty-four hours, that is, has it's inftant of noon.
Latin.
Metaphysics, otherwife called Ontology, the Science of the af-
fections of being in general. It employs abJlraSi reafoning.
Turn to the word Abstract. Greek.
Meteorology, the Science of Meteors, that is, of bodies floating
in the air, and quickly patting away. Greek.
Microscope*
AND SCIENTIFIC TERMS. 497
Microscope, an optical inftrument, which, by means of a greatly-
magnifying glafs, renders diftinctly vifible objects too mi-
nute for the unaffifted eye. Greek.
Minor, in Logic, the fecond, or particular propofition of a fyl-
logifm : for example, in this Syllogifm,
.All men are mortal :
But, The King is a man ;
Therefore, The King is mortal.
The firft propofition, All men are mortal is the Major;
the fecond, the King is a man, is the Minor, and thefe two
are called the premifes ; the third, the King is mortal, is the
conclufion. Latin;
Mobility, eafinefs of being moved. Latin.
Mode, in Logic, particular form or ftructure of argument,
Latin.
Monad, a minute particle of matter which admits of no farther
fubdivifion. Greek.
Monochord, a mufical'inftrument of one firing. Greek.
Myops, fliort-flghted. Greek.
N.
Nadir, the Point in the heavens directly under foot. Arabic,
Navigatipn, the art of failing. Latin.
Negation, denial, the oppofite of affirmation. Latin.
Notion, thought ; reprefentation of any thing formed by the
mind. Latin.
O.
OBjECTiVE-lens, in Optics, that glafs of a telefcope which is
turned to the objedt or thing looked at. Latin.
Oblique, not direct, not perpendicular, not parallel. Latin;
Vol. II, Kk Observatory,
4^8 GLOSSARY OF FOREIGN
Observatory, an edifice reared for the purpofe of aftronomical
obfervations. Latin.
Occult, fecret, unknown, undifcoverable. Latin.
Octave, in Mufic, a regular fucceffion of notes from one to eight;
the firft and the eighth having the fame name and emitting
the lame found. Latin.
OcuLAR-lens, in Optics, that glafs of a telefcope which is applied
to the eye. Latin.
Opaque, what does not tranfmit the rays of light, not tranfparent.
Latin*
Optics, the Science of the nature and laws of virion, ox fight.
Greek.
Orb, fphere, heavenly globular body. Latin.
Or3it, the circular path in which a planet moves round the Sun.
Latin. '
Oscillation, alternate moving backward and forward like the
pendulum of a clock. L^tin.
P.
Paradox, a tenet which exceeds or contradicts received opinion,
affirmation contrary to appearance. Greek.
PARALLEL-lines, in Geometry, lines which through the whole of
their length maintain the fame diftance : they are the op-
pofite of convergent and divergent. Greek.
Parallelism, ftate of being parallel.
Parallelogram, a geometrical' figure of four fides, having this
property, that the oppofite fides are equal and parallel, and
the oppofite angles equal. Greek.
Pellucid, what tranfmits the rays of light : tranfparent. Latin.
TPendulum, a heavy body fufpended, fo as to fwing backward and
forward without obftruftion, for the purpofe of meafuring
time :
AND SCIENTIFIC TERMS. 499
time : the great perfe&ion of fuch an inurnment is, that
every vibration or fwing fhall be performed in exa&ly the
fame quantity of time. Latin.
Perception, the power of perceivings knowledge* confcioufnefs.
Latin.
Permeable, what may be pafled through. Latin.
Perpendicular* in Geometry, one line ftanding on another, ot
on a horizontal plane, without the flighteft inclination to
one fide more than another, and forming right angles with
the horizontal line or plane. Latin.
Phalanx, a military force clofely embodied. Latin.
Phasis, appearance prefented by the changes of a heavenly body,
particularly thofe of the Moon. The Greek and Latift
plural p/iqjls is adopted in our language.
Phenomenon, ftriking appearance of Nature. The Greek plura
phenomena is in common ufe.
Philosophy, knowledge natural or moral : Syftem in correfpon-
dence to which important truths are explained : Acade-
mical cOurfe of Science. Greek.
Physics, the Science of Nature; natural Philofophy. Greek.
Piano, in Mufic, foftly, delicately, oppofite to forte. Italian.
Piston, the moveable circular fubftance fitted to the cavity of
a tube, fuch as a pump or fyringe, for the purpofe of
fuftion, expulfion, or condenfing of fluids. French.
Planet, a wandering ftar ; thofe heavenly bodies, our globe being
one, which perform a regularly irregular courfe round the
Sun, are called planets, Greek.
Plano-concave, in Optics, a glafs which has one furface plane,
and the other hollow. Latin,
Plano-convex, an optical glafs which has one furface plane, and
the other raifed. Latin.
Plenum, fpace filled with fubftance. Latin.
K k z Plumb-line,
50O GLOSSARY OF FOREIGN
Plume-ltne, a weight appended to a firing, for the purpofe of
afcertaining perpendicularity.
Polar-Circles, circles parallel to the Equator and the Tropics,
at the diftance of twenty three degrees and a half each
from it's refpective Pole. Latin.
Polarity, tendency toward the Pole. Latin.
Polygon, a figure having many fides and angles. Greek.
Polytheism, the doctrine of a plurality of Gods. Greek.
Porous, full of fmall minute pafTages. Greek.
Presbytes, far-fighted. Greek.
Prescience, foreknowledge. Latin.
Predicate, in Logic, what is affirmed of the fubjecr., as, man is
rational. Latin.
Predilection, preference given from pre-conceived aff'eclion.
Latin.
Pre-established harmony, the metaphyfical doclrine of an
original adaptation of mind to matter, by a creative act of
the Supreme Will, in virtue of which every human action
is performed.
Prism, a triangular optical inftrument of glafs, contrived for the
purpofe of making experiments with the rays of light.
Greek.
Problem, a propofition announcing fomething to be firft per-
formed and then demonstrated. Greek, *
Proboscis, the fnout or trunk of an elephant or other animal.
Latin.
Prominent, jutting out, projecting forward. Latin.
Proposition, a point advanced or affirmed with a view to proof.
Latin.
- Proximity, nearnefs. Latin.
Pupil, in Optics, the apple of the eye. Latin.
Pyrometer, a machine contrived to afcertain the degree of the
expanfion of folid bodies, by the force of fire. Greek.
Pyrrhonist,
AND SCIENTIFIC TERMS. 501
Pyrrhonist, an univerfal doubter and unbeliever; derived from
the name of the Man.
Q.
Quadrant, the fourth part of a circle; an inftrument of that
.form, contrived to meafureand afcertain Latitude. Latin.
Quadrilateral, confiding of four fides. Latin.
Quotient, in Arithmetic, the number refulting from the divifion
of two numbers which meafure each other. Thus on di-
viding 36 by 4, we have a quotient of 9.
R.
Radius, in F.nglifh ray, a ftraight line drawn from the centre of a.
circle or fphere to the circumference. The Latin plural
radii is in ufe.
Rarefaction, the rendering of a fubftance thinner, more trans-
parent, it is the oppofite of condenfation. Latin.
Ratio, proportion. Latin.
Ratiocination, a procefs of reafoning, a deduction of fair con-«
clufions from admitted premifes. Latin.
Recipient, that which receives and contains. Latin.
Reciprocally, mutually, interchangeably. Latin.
Rectangular, containing one or more right angles. A ri^ht
angle confifts of 90 degrees. Latin.
Rectilinear, confifting of ftraight lines. Latin.
Reflection, in Catoptricks, the fending back of the rays of light
from an illuminated body. Latin.
Reflux, the ebbing, or flowing back, of the tide. Latin.
Refraction, in Dioptricks, the deviation or broken off'courfe of
a ray of light on pafling obliquely from one medium
K k 3 through
502 GLOSSARY OT FOREIGN
through, another, as from air through water or glafs.
Latin.
Refrangibility, difpofltion to leave the direft courfe, capability
of being broken or refracted. Latin.
REFRiNGENT-medium, that which alters, or breaks off, the courfe
of rays. Latin.
Reminiscence, the power of recollection, memory. Latin.
Repulsion, the act. or power of driving back. Latin.
Resinous, confifting of, or fimilar to refin, the fat, fulphureous
emanation from certain vegetables. Latin.
Resonance, found repeated. Latin.
Respiration, the act. of breathing. Latin.
Reticulated, formed like a" net. Latin.
Retina, the delicate, net-like membrane at the bottom of the
eye, on which are painted the images of the objects which
we contemplate. Latin.
Retrograde, moving in a backward direction. Latin.
Reverberation, the acl: of beating or driving back. Latin.
Revery, loofe, wild, irregular meditation.
s.
Satellite, an inferior, attendant planet revolving round a greater.
Latin.
Scalpel, a chirurgical inftrument ufedfor fcraping a bone. Latin.
Science, knowledge : in the plural, the feven liberal arts, namely,
Grammar, Rhetoric, Logic, Arithmetic, Mufic, Geome-
try, Aftronomy.
Segment, in Geometry, part of a circle formed by a ftraight line
drawn from one extremity of any arch to the other, and
the part of the circumference which conftitutes that arch.
The ftraight line is denominated the chord of the arch,
from it's reiemblance to a bow-ftiing. Latin,
Semicircle,
AND SBIENTIFIC TERMS. 503
Semicircle, the half of a circle; the fegment formed by a dia-
meter as the chord, and one half the circumfetepce as the
arch. Latin.
Semitone, in Mufic, half a tone, theleaft of all intervals admitted
into modern mufic. The j'einitonc major is the difference
between the greater third and the fourth, it's relation is as
15 to 16 : the J'emitone minor is the difference of the greater
third and the lejfer third, and it's relation is as 24 to 25.
Latin.
Sensation, perception by means of the fenfes. Latin.
Series, regular, fettled, proportional order or progreffion, as, m
numbers, 9, 18, 27, 36,45, 54, 63 are in a Jerics. The
word is the fame Angular and plural. Latin.
Seventh, in Mufic, the inverted difcordant interval of the Second,
called by the Ancients Heptaehordon, becaufe it is formed of
feven founds. There are four forts of the feventh, of 'which
the following are the proportions in numbers; as 5 to 9 :
as 8 to 15: as 75 to 128 : as 81 to 160: it is harm and
unharmonious.
Solar-tide, the flux and reflux of the tide relatively to the Sun.
Latin.
Solution, demonftration, clearing up of intricacy or difficulty.
Latin.
Sonorous, emitting loud or thrill founds. Latin.
Species, kind, fort, ckifs: fee Genus. It is the fame in Angular
and plural. Latin.
Spectrum, an image; a vi Able form. Latin.
Sphere, Globe. Greek.
Spheroid, approaching to the form of a fphere, but fomewhat
lengthened. Greek.
Spiritual, not confiding of, diftincr. from matter or body. Latin.
Sublime, elevated in place; in Chymiftry, raifed by the force of
Are. Latin.
Subterfuge,
5©4 GLOSSARY OF FOREIGN
Subterfuge, mean, paltry efcape or evafion. Latin.
Subterraneous, under the furface of the ground. Latin.
Subtile, thin, not denfe, not grofs. Latin.
Superficial, external, extended along the furface. Latin.
Supernatural, what is above or beyond the powers of Nature.
Latin.
Surface, in Geometry, length and breadth without thicknefs.
French.
Syllogism, in Logic, an argument confuting of three propo-
rtions : for example, Every virtue is commendable : honejly
is a virtue ; therefore honejiy is commendable. See Major and
Minor. Greek.
System, a fcheme of combination and arrangement, which re-
duces many things to a regular connection, dependance
and co-operation. Greek.
T.
Tangent, in Geometry, a ftraight line touching a circle exter-
nally in a fingle point. Latin.
Telescope, an optical inftrument defigned, by the magnifying
power of glaffes, to reprefent difiant bodies as much nearer.
Greek.
Temperament, ftate of body or mind as produced by, or depend-
ing upon, the predominancy of aparticular quality. Latin.
Tension, the ftate of being ftretched out, wound up, diftended.
Latin.
Tenuity, thinnefs, delicate flnenefs. Latin. «
Term, defcriptive nairie, or phrafe; component part, condition.
Latin.
Terraqueous, confuting of land and water. Latin.
Theology,
AND SCIENTIFIC TERMS. 505
Theology, fyftematic Divinity. Greek.
Theorem, a propofition announced for demonstration. Greek.
Theory, a doctrine contemplated and conceived in the mind, but
not yet confirmed by irrefiuible argument, or fatisfying
experiment. Greek.
Thermometer, an inftrument contrived to meafure the heat of
the air or other body by means of the riling or falling of a
fpirituous fluid. Greek.
Third, in Mufic, the firft of the two imperfect concords, fo called
becaufe it's interval is always compofed of two degrees or
of three diatonic founds. The tierce major or greater thirds
is reprefented in numbers by the ratio of 4 to 5 : and the
lejfer, by the relation of 5 to 6. See Vol. II. Let.. VI.
and VII.
Tide, the alternate riling and falling of the Water in rivers, and
along the fhoresof the Sea. Saxon and Dutch.
Tone, in Mufic, the degree of elevation which the voice aflumes,
and to which inftruments are adapted, in order to the har-
monious execution of a mufical compofition : a pitch pipe.
Latin and Greek.
Transit, in Aflronomy, the paffing of one heavenly body over
the diflc of another. Latin.
Transmission, permiflion to pafs through. Latin.
Transparent, clear, what may be feen through, as air, water,
glafs. Latin.
Transverse, in a crofs direction. Latin.
Triangle, a geometrical figure confifting of three fides and three
angles. Latin.
Tube, a pipe; a long hollow body. Latin.
Tunicle, afmall coat or covering. Latin.
Vacuum,
506 . GLOSSARY OF FOREIGN
v*
Vacuum, empty fpace. Latin.
Valve, a moveable membrane in the veffels of an animal body,
and imitated by art in the conftruCtion of various machines,
which opens for giving paffage to fluids in one direction,
but fhuts to oppoie their return through the fame paffage.
Latin.
Velocity, fpeed, fwiftnefs of motion. Latin.
Vertical, perpendicularly over head. Vertical angles, in Geo-
metry, are thofe formed by the interferon of two ftraight
lines, in whatever direction, making four in all at the point
of interferon, and of which the mutual two and two are
equal. Latin.
Vibration, rapid, tremulous motion backward and forward.
Latin.
Visual, relating to vifion or fight; belonging to the eye. Latin.
Vitreous, compofed of, or refembling glafs. Latin.
Vivid, lively, brifk, fprightly. Latin.
V.
Ultimate, final, beyond which there is no farther progrefs,
Latin .
Unison, emiflion of the fame or harmonious founds. Latin.
Untenable, what cannot be maintained or fupported.
W.
Waning, gradual diminution of apparent magnitude and light.
Saxon.
6 Waxing,
AND SCIENTIFIC TERMS. 507
Waxing, gradual increafe of apparent magnitude and light; par-
ticularly of the Moon. Saxon and Danifti.
Wind-gun, a gun which forcibly emits a ball by means of com-
preffed air or wind.
Z.
Zenith, the point in the heavens dire&ly perpendicular or ver-
tical : exa&ly over head : the oppofite of Nadir. Arabic.
T. Giilett, Printer, Salisbury-square.
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